Can I temporary use battery booster as a car battery?

Something is wrong with either my alternator or the cables connecting
alternator/battery/etc. I have no idea when the previous owner replaced
them. (Or perhaps never did)
Yesterday I realized that my battery light is on indicating it's not being
properly charged while driving. I found out that the screw that connects the
cable behind the alternator had fried (melted) and so the cable is
disconnected.
While I have some time this weekend to take a deep look into it and see
what needs to be replaced, here is my question:

Since my car is not charging the battery, I'm using it now but god knows
when it will die. When that happens, will it be possible for me to use my
portable battery booster temporarily as my car battery? It's a lot easier to
charge the booster every night than finding a place to charge my battery (I
don't own a battery charger but even if I do, I live in an apartment with no
garage)