|Feasible? Yes. Possible? Yes. Reasonable? A (qualified) yes.
CELTA TBI tends to be somewhat less expensive than those provided elsewhere. The difference would go quite a way toward covering your living costs. Aim for accommodation in the Kuningan area. You don’t want to be dealing with too much traffic. Generally, it’s just a nice area. As far as possible, don’t skimp on your lodgings (during the course, at least).
If you’re not totally set on the idea of working for a TBI in Jakarta there’s every chance that you’ll get an offer on employment at one of their other branches. And it doesn’t have to be TBI, does it?
I won’t rattle on about any of this. In short, I think it sounds like a decent idea well-posted. Good thinking! And good luck.