electrician here, the answer to your question is...no, you wont burn the place down but you will blow a fuse or trip the breaker.
If the 2 ourlets your talking about are in the same room, then more than likely they are on the same circuit (20 amp fuse or breaker).
A 20 amp circuit is rated fo around 2300 watts max(I think). So if those 2 outlets are the only outlets on the whole circuit (which I highly doubt) then you would be maxed out right off the bat with just your lighting.
Is your breaker box in your apartment, if so, Id suggest adding a 20 amp breaker to the box, that way you could have a designated circuit just for your lighting for your grow.....good luck....