I switched to airless years ago so my recollection of air sprayers is a little foggy. First, you don't use 90 psi for spraying, I think it is 40 psi or a little higher. You will probably be marginal have have to wait for catch up but if you tank is big enough and the dresser small enough you could be fine.
If you haven't bought the spray gun yet, look at the HVLP guns. They seem to be all the rage now. HVLP stands for High Volume, Low Pressure. That should work better for you.