Both will sound great, so the answer is "yes."
I personally don't see much point in renting Neves when you've got a pair of APIs right there.
As far as sound differences, API pres tend to feel punchier and they seem to bring out the mids and highs just a bit more, with the lows feeling tighter and less prominent than with the Neves. In my experience, Neves (1272 and 1073 style) tend to feel a bit thicker and more substantial, but aren't quite as punchy as the API. Now, these are what I'd call "engineer-y descriptions on the internet," meaning that the average person probably wouldn't hear the differences anyway, as they are definitely subtle.
So yeah, use your APIs.