The 'origins' of the Latins is not entirely well understood, at least in a linear fashion. There certainly was some mixing of Celts into Italy, particularly in the North (Liguria in particular).

The problem here is that determining the origin of these Proto-cultures is a bit of a....tricky business. There are two primary ways that archaeologists and historians can do this. One is to categorize the material culture of an area. This gives us a farther window to look into, in that it allows analysis that predates literacy. Things like tool types, home construction patterns, and material usage are all big components of categorizing these types of cultures. However, if a type of 'material' culture appears in one place, and spreads to another, is it evidence of migrating peoples or simply migrating technology? There is evidence of early ancestors of what almost certainly became the Latins adopting material cultures from north of the Po, areas that we are pretty sure contained a Celtic, or at least Celtic infused culture at this time.

The other way we can try to piece the language history together. It is this method that has allowed some to speculate on the geographic origins of the 'Indo-European' peoples originating from the Caucus region (see this map: http://upload.wikimedia.org/wikipedia/commons/5/5a/IE_expansion.png). However, with the Latins (as with the Greeks) the evidence is largely subjective. For example, say you find a word in Latin that appears to have Celtic origins? Does that mean the Celts moved into Latium, or that the Romans merely adopted a word from them?

At any rate, coming back to the original question: were Romans simply Hellenized Celts? This would imply that their material culture and language have heavy Celtic influence, to the point that it should be clear. The reality is that this simply isn't the case, at least from the evidence we have. The best evidence we have is that the Latin tribes probably existed in the region of Latium since at least the 2nd millennium BCE, and most of the Hellenization that occured early in their 'literary' history was through Etruscan influences.

This seems to me to be a bit of an overcorrection of past summations of Roman-Celtic relations that marginalized Celtic contributions. There was a great deal of mutual influence between Roman and Celtic culture due to the heavy presence of Celtic populations in northern Italy--such fundamental words as caballus (the common term for horse), cambio, -ire (vulgar term for "to barter"), lepus (hare), and possibly auriga (charioteer) and nauta (sailor). They certainly interacted frequently, and a perception of many past scholars of the Celtic peoples as being barbarous and uncivilized obscured the degree to which this interaction was not merely wartime. But to say that the Romans were Celtic themselves is a bridge too far.