It will cause the print to warp ans split as you are cooling the outside faster than the inside. The ideal condition for ABS is a closed system where you can keep the ambient temp high so the part cools evenly inside and out.
As for the bed it might warp it as the edges will cool faster as well. But once uniform in temp it should return to it's normal shape.
Honestly I would learn to print PETG if I where you. It's just as durable if not more so than ABS and does not require all the temperature management hassle. It also has very little if any odor during printing. You just have to get used to slower printing as it does require slower speeds. But it has all the benefits of ABS without the hassle.
Printing since 2009 and still love it!
Anycubic 4MAX best $225 ever invested.
Voxelabs Proxima SLA. 6 inch 2k Mono LCD.
Anycubic Predator, massive Delta machine. 450 x 370 print envelope.