USB charger have as much "power" as you put into it, in range of sanity values for microUSB pins (which is much more than we need, anyway). Possibility to run without battery (or lack of) depends on charging chip/circuicity.

Which leads to my question - what is max charge current supported in GTA04/that is going to be used on Neo900? Is here hope to charge with 1250 mA like with (software side tweaked) N900?

Of course if not, it isn't any major dealbreaker - it's just interesting for dual-cell battery builders, as from battery's perspective, much higher charging current are acceptable (if device's chips permit it and doesn't fry) and desirable (due to charging time decrease with 3Ah capacity, or more).
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Super-huge congratulations on such awesome result of completed crowd-funding stages! I really regret that I'm financially unable to pre-order (my small "for love of project" donation must be enough, for now), as involvement in other project left me flat-out broke. I hope I'll be able to catch up with some far-future batches, should they happen!

/Estel