This is a supremely interesting question, and I fear it isn't quite getting the attention that it deserves because of the popular perception of the Underground Railroad. The idea of the Underground Railroad looms very large in popular culture and popular history about slavery and the struggle for freedom in the United States; Wikipedia indirectly (because Wikipedia is aggressively useless at these things) cites James Banks' claim from March Toward Freedom: A History of Black Americans that about 100,000 people made use of some kind of organised network to escape slavery through the course of the 19th century. There is a perception in popular culture I think that the Underground Railroad existed as this extremely well organised and well supported institution that fought the good fight against slavery, and that this is something historians have spent a lot of time working on.

Whether by design or accident, the term Underground Railroad itself definitely conjures the image of something that has to be very carefully organised and managed; an elaborate network of pathways and stopovers that someone has to supervise travel along, with multiple on and off boarding points and a regular rolling operation. The truth is that the Underground Railroad, although it certainly existed in some form, is something of an invention of popular history. It appears in the historical record in quite a tenuous and confusing fashion. The actual evidence we have in the historical record for the scope, nature and organisation of the Underground Railroad is quite lacking. Historians of quite different stripes have gone looking for evidence of an institutionalised Underground Railroad and have struggled to turn up a substantial body of evidence for one, and there seems to be a deficit of plausibility in some local folklore stories when we consider the evidence we do have for what a locality was like in the 19th century.

The historical reality is rather less glamorous than the popular history we see today. The use of the term Underground Railroad appears to be less an accurate metaphor and more of a euphemism for illicit travel. There was certainly no such thing as a national or even state-wide organisation or movement that we can describe as the Underground Railroad, and works that describe people as 'agents' or 'officers' of the Railroad very much appear to be exaggerating the extent to which the enterprise was a well organised and hierarchical one. Instead, what we think of as the Underground Railroad is best understood as a map of impermanent, very localised networks that could - if they aligned at the right times and in the right places - be exploited by people escaping slavery. It was a chaotic and ephemeral thing, not well-oiled machine or effective human institution.

And that makes it very difficult indeed to distinguish between enslaved people who we might describe as having escaped with the Underground Railroad from those who escaped 'separately'. You can make the argument that the Underground Railroad is simply a euphemism for the act of escaping slavery itself, in which case every enslaved person who successfully fled from his or her purported owners escaped via the Underground Railroad. Alternatively you could limit the understanding of the Railroad to encompass only those enslaved people who benefited in some way from assistant by organised anti-slavery activity, or from the assistance of sympathetic white people with anti-slavery sentiments.

If you want to cut it in one of those latter ways, then it's very difficult to give you an estimate of how many enslaved people escaped with or without the assistance of something we could perhaps describe as the Underground Railroad. Whilst we can reasonably conclude that thousands of individual men and women were able to escape from the South and from slavery during the course of the 19th century, we do not know the individual particulars of the vast majority of cases. And whilst there is a rich body of contemporary accounts of the experience of slavery, the vast majority of these were written by white abolitionists on behalf of enslaved black people - and they were written with the political purpose of persuading white audiences of the injustices of slavery and the wrongness of support for or apathy towards it. We cannot easily say how many accounts of white people helping fleeing slaves in a very substantial way reflect historical reality and how many represent embellishment to make a narrative that would be more appealing to white readers in the 19th century; it absolutely happened, but we have no way of approximating scale.

We do certainly have accounts of people escaping from slavery substantially or entirely under their own power however. In The Dark Deeds of American Slavery Revealed, which is the alternate title of the narrative attributed to a formerly enslaved man named William Anderson, the author describes Anderson escaping with the help of another slave by forging free movement papers so he could quite literally walk off the estate and stowing away on a boat. Henry 'Box' Brown is alleged to have escaped via a plot that, though benefited from outside help, was entirely of his own quite ingenious making. Lewis and Milton Clarke took advantage of the limited liberties given to them by white masters to pass themselves off as a band of travelling musicians, and escape that way. Ellen and William Craft famously escaped by the lighter-skinned Ellen passing herself off as a white slave owner, dressing up as a man so she was less recognisable. So yes, there were certainly enslaved people who escaped without the aid of the Underground Railroad - but that is perhaps less impressive when we consider that the Underground Railroad was not really a thing as we understand it in popular culture today.

It's worth giving some thought too to where our flawed popular concept of the Railroad has come from. The earliest accounts of the Railroad were constructed largely in the latter half of the 19th century by ageing abolitionists and white writers who wanted to tell a compelling story of the struggle against slavery. In the life narratives of formerly enslaved people themselves, we find that the idea of the Underground Railroad as a distinct entity tends to only appear in biographical works that were published after the US Civil War and the abolition of slavery. Often when accounts of people escaping slavery written before the Civil War are described as talking about the experience of the Underground Railroad that terminology does not actually appear in the original text. You will find it much easier to find material about the Underground Railroad being discussed in those explicit terms after the end of the Civil War than before it, and there's a good reason for that.

The historian Wilbur Siebert published a highly influential book in the 1890s called The Underground Railroad from Slavery to Freedom which was substantially based on an appeal to information from people who claimed to be involved with such an institution, without much critical inquiry into the claims being made. His book played a big role in cementing the idea of the Underground Railroad as a well organised endeavour. The work of white writers like Siebert, combined with the increasing distortion of popular folklore as abolition increasingly became recognised as a moral good in the decades after the end of the Civil War, helped to create the impression in popular culture that the Underground Railroad was this truly vast institution. Black writers like William Still in his The Underground Railroad: A Record (1871, I think) broadly gave a very different impression of a haphazard and chaotic system, and indeed Still includes the example of the Crafts - who made most of the journey to freedom entirely independently - as an example of a successful Underground Railroad journey.

Larry Gara published a book called The Liberty Line in 1961 that essentially challenged this view and picked apart Siebert's flawed research, arguing that if the Railroad could be said to exist it was in that much more diffuse and disparate fashion. Gara also criticised the Railroad image for privileging the idea that white anti-slavery activists were the driving force behind making escape from slavery possible, and sought to draw greater attention to the agency of enslaved people and to the support that free black communities gave to fugitives fleeing slavery. Some have criticised Gara for being a bit too keen to downplay white involvement, but the fundamental point remains a sound one when we consider the popular image of the Underground Railroad that still persists today. Since Gara there hasn't really been anything that I would describe as an authoritative study of the Railroad phenomenon in particular, and though we have had some recent contributions to the scholarship that problem of scarce sourcing remains. Cheryl LaRoche wrote a book a few years ago called Free Black Communities and the Underground Railroad that does pretty much what it says on the tin. It's well-researched and thought-out with some very profound insights (particularly her descriptions of the Underground Railroad as a phenomenon in cultural memory comparable to other mass migrations, forced or otherwise, of people of African descent). I feel she's a bit self-contradictory in trying to come to a conclusion about just how well organised and networked the Railroad phenomenon was, but it's a good read on the whole (and LaRoche is someone who on the whole I think has a very good moral approach to the study of slavery).