Dear Jason,
At Mabtech we do rest our cells for 1h in the incubator following thawing of cryopreserved PBMCs. Cells destined to die fall down to the bottom and you can continue seeding your ELISpot plate with cells that have a higher proportions of cells that will make it through the entire incubation.
The dead cells that fall to the bottom of the tube often leak out DNA, that get tangled up with other cells and you get clumps. These should be removed in my opinion. Especially since you need single cells to go into the ELISpot plate, and not clumps of cells, because then you will get confluent blobs of spots.
One thing that I have heard about is that you should "wash" the remaining clumps with new cell culture medium after you sucked off the "good supernatant". The thinking is that living cells have gotten "tangled" up in the mesh of dead cells, apoptotic cells and DNA strands. By adding fresh medium to the clumps, resuspending up an down a couple of times with a pipette, you can dissloge good cells for downstream use. Worth a try.
Using Trypsin-EDTA for the purpose of removing clumps I have personal experience with and not heard about. I have on the other hand been given recommendation to use DNAse in order to brake up the DNA strands from dead cells. This should inhibit clump formation. I have not tried it myself but sounds reasonable.