Yes or no? If so, how and when is best?
Best time to divide thyme is in spring.
Here is a link that might be useful: how to divide thyme
If you have a creeping thyme, it roots along its branches sometimes. You can pile a bit of dirt on it in the spring or summer to encourage it to put down some roots. Divide it with a sharp trowel or spading shovel. I transplated some in the summer from my old garden and it looks terrific right now (and much happier in its new home).