First: Ivy league programs are not necessarily the best choice for your particular sub-discipline when it comes to graduate studies. What matters is fit with the department and, most importantly, with the professor who will be your adviser. Additionally, programs are generally reluctant to take students fresh out of undergraduate and lacking real-world experience.

Second: Undergraduate school does not particularly matter, but coming from a strong history program does. That said, many people get MA degrees before they start PhDs, and it is a common way to atone for one's undergraduate sins, whatever they might be.

Third: It is certainly the case that top-tier schools (of which, depending on focus, the Ivies are a subset), are the most likely to place their graduates in tenured positions at other top-tier schools. However, the PhD job market is pretty rough, although history isn't so bad, with approximately 50% of History PhDs in the past 10 years ending up in a tenure-track position according to a recent study by the American Historical Association. A 50% employment rate is pretty terrible for 10 years of study.

Some people will say the answer is no, but in reality if you look at the demographics of the people who get into Ivy League grad programs, a disproportionate amount come from Ivy League schools. Of course this topic is debatable, but the reality is, no one can be completely sure what the answer is aside from the admissions committees at these Ivy League grad programs.

I would say, just go to the best school that you can for undergrad. The reputation will matter to an extent. They will clearly prefer someone with an undergrad degree from an Ivy League with a 3.4 GPA over a University of Phoenix grad with a 3.5 GPA.

Remember that humans are evaluating the applications, and they're not robots. They will look at the school you went to and that may affect their decision consciously or subconsciously.