I have not yet learned about a limit and can tell that a few thousand are no problem. I have a eight cores and lots of RAM. It may slow down your machine or rather your graphics once the model gets too complex, though it will need quite some load until this gets apparent.
Part quantity is not the only factor, I'd rather say model complexity. While a complex model like a very detailed car body made up of only a dozen parts may have effects on speed, handling a few thousand simple cubes may be no issue.