Can I cut carpet tiles with a table saw?
As already noted in a comment, this is likely to end in quite a mess. And could be a bit dangerous too.
A quick search confirms my hunch about the right way: score the back and cut with a utility knife. A new knife and a pack of blades cost very little.
Reminds me of a cute anecdote in a DIY magazine I saw once about someone ending up with dust everywhere from cutting drywall with a circular saw. Who then found out that everyone else just scores and cuts with a utility knife. Carpet tile may be a little tougher, but it is not the type of hard material that a saw cuts well (and that a knife doesn't cut at all).
In response to the latest question edit:

I'm not seeking advise how to optimize cutting carpet with a knife. The post is to collect input on the specific question.

The simple answer is: Yes you could, but please don't!