Can you? Sure, but as noted in the comments, it's probably not the best idea. Even with a zero clearance insert in your table saw, you're likely to get threads caught in a tooth, instead of being cut, and those threads will wind around the saw arbor, bind it up and destroy your carpet square. On the bright side, the ZCI should prevent the carpet itself from being pulled into the saw.
You're cutting carpet tiles, so they're pretty small.
Drop a piece of plywood, larger than your tiles, on the floor as your cutting station.
- Use a workbench if you want, but on the floor means you can put your upper body weight on it, not just your arm.
Measure & mark each tile
- You could screw down a straight piece of 2x4 as a guide to hold the edge.
Hold a steel rule on top as a guide
- If the tiles are all to be cut to the same dimension, pre-measure and put marks on the 2x4 to align the rule to.
- Go all out and drive a couple of screws/nails to slide the rule against as a stop for even greater speed in aligning everything.
- If you're very careful, you could put the screw/nail right at the edge of the carpet tile so you've got the tile held between the 2x4 and the 2 nails, drop the rule on the correct side and everything is set up and ready to cut with no effort to do the alignment, and the square mostly held in place for you.
Have at with a sharp blade. You'll be quite pleased at how quickly it cuts.
The plywood is big enough that you don't have to worry about aligning the cut over it, it'll support the whole piece of carpet.
When the cutting gets tough, replace the blade.
Just as fast and safer than trying with a power tool.
The only power tool I'd actually consider trying would be powered shears which work like a pair of scissors. A table or band saw risks drawing fibers into the mechanism, potentially binding it, while a scroll-saw, even with the heaviest blade you could find, would probably snap blades faster than it cut the carpet.