Does anyone know if the SIRT training pistols will register hits on Laserlyte Targets?

Yes they will. I bought the cans, I wish I went with the bullseye.

Only the red laser SIRT models are reliable with the trainer. The green laser models don't work so well.

Only the red laser SIRT models are reliable with the trainer. The green laser models don't work so well.

 

If it's a model that has both green and red lasers, one to indicate when the slack is out of the trigger and one to register hits, they can be switched so the red one hits the target.  

 

The bullseye targets are good.  Looks like they addressed the issue of its being annoying to reset the cans with these:

https://www.laserlyte.com/products/rumble-tyme-laser-trainer-target

If it's a model that has both green and red lasers, one to indicate when the slack is out of the trigger and one to register hits, they can be switched so the red one hits the target.

Correct

I ended up going with the quick time model, I figure it will be the most beneficial to me with presentation drills.

I use mine all the time for dry fire practice. Mostly holster draws and mag changes. I have placed a piece of masking tape over the front so I see no dot on the target. I find the dot very distracting and it takes my focus off the front sight. I tend to look over the front sight and search for the dot if its visible. Not good. To each his own.

I ended up putting together my target today. I used a mannequin torso and cut out a square in the chest. I then made a hook inside of the mannequin to hold my quick tyme. Works great for presentation drills.