sounds like homeless is not an issue -- but how she became homeless.
So I guess my question is -- do you want to date a drunk? Now I am assuming she is drinking too much not like a one time getting drunk. If it is an ongoing issue then she needs help on dealing with it.
As far as having problems getting a job, I think you need to know why --- is it really just difficult to get a job (which it has been) or is it she is being too picky on a job, or has losts jobs in the past due to her prior performance.
Being engaged twice could be a red flag especially twice in one year -
To be honest she sounds unstable. Not because of being homeless, but it sounds like she is homeless because of her issues, not just being in a bad luck situation. If that is the case, then decide for yourself if she is worth all the baggage.