You can do it. Only problem shooting sporting with a pump is that due to the light weight of the gun they have a tendency to beat up shooters over the course of multiple rounds. That's why we don't recommend using them for women and children. As for a "slam fire", wouldn't recommend that as it's not conducive for breaking targets.
I've done it in the past, and what will more than likely happen, is you will "short stroke" your fair share of hull ejections. You try to rack that second shell in haste, and don't fully eject. Can be done though
I shoot 5 stand and trap doubles with a few guys who use pumps. They do very well. The pump is not a handicap for them.
I have an older Model 37. It does not have a trigger disconnect. Mine will "slam fire". Newer Model 37s may not.
Try this. Clear your SG. Dry fire it. Do not release the trigger. Pump it. Then release the trigger and pull it. If it goes off it has a trigger disconnect. If it does not go off then it went off when you slammed the action forward and it would result in a "slam fire" if it was loaded.
The only disadvantage of any shotgun is not being comfortable with its use. My first shotgun, 48 years ago is a model 37. It Can only be described as slick and quick. I can shoot it almost as quick as any other shotgun. Of coarse it will slam fire when I want it. Never has when not.
Of coarse there are always better tools to use for a particular job, but don't let that stop you from going out if that is the only gun you have.