One question to consider with this, is are the majority of visitors to your homepage returning users (and therefore looking to log in) or are they new visitors that you want to sign up?
If you’re skewed heavily in one direction, go for that (e.g. if 90% of visitors don’t already have an account, you probably dont’ need to login form on the homepage, because focus should be on signing up). If it’s 50-50 or more for returning visitors, the log in on the homepage would certainly save hassle for a significant number of users, so as long as it’s done unobtrusively to those who don’t need the login form, it seems like a good idea to have it on the homepage.
If you’re a new app looking to build up user numbers, the focus should be on one main sign up button, and an additional form or button that could pull focus from that is best to avoid.