Well thanks for the correction. Thant really makes sense in theory.
But on practice few of my friends were successfully enrolled to colleges and universities of NYC with pending asylum and no other status in background(visas were expired).
You have NO RESIDENCY IN THE USA, but you can be resident of the state in non-law mention i.e. for DMV just because you're living there.
The law doesn't define well this section since there is a possibility of you being illegal or legal, as you said and that's correct but if you're not under removal proceedings then you're awaiting for your hearing as legal alien. You have EAD, SSN and possibility to travel abroad with advance parole. These are more likely attributes of legal status(or how it can be called) rather than illegal even if the law doesn't define this uniquely.
In other words there are no problems to apply in NY area. As of other states I do not know maybe they use other rules.
Does anybody have negative experience while applying to the colleges with i589 pending?