I'm not sure about thyme, but I have moss growing in the 1/8th inch crack between installed bricks in my front path.

No, they're not too close. Plants can grow in the tiniest of fissures. But you'll have to start from seed or extremely small plants.

Is this the main front walkway? If so, the plants will grow irregularly where people walk, and some folks may find the bees that are attracted to blooms disconcerting. And for anyone with a mobility issue such as balance problems or needing a cane, as well as anyone in heels, this will be a difficult surface to walk on. As someone with elderly parents as well as a friend with balance problems, this has become more of a concern to me. Just a consideration if this is the main door for visitors. I love this type of surface on less traveled walks.

How much light does the area get? Thyme needs full sun.

I was answering the basic question, "will they grow?" Rather than will they spill over the stones or is it a good place to grow them. My whole garden is paved and there are plants growing all over it but it isn't a thoroughfare. I shear the whole area down a few times a year and where we walk to the shed the plants don't grow very big. I actually think the gaps are too big in places because they'll fill up with weeds long before the thyme can spread throughout.

And if the soil is not the lean and dry type that thyme wants the planting probably won't be low maintenance at all, because you will be likely to have weeds sprouting in it. With getting these out of the fabric-like thyme the most tedious of chores - especially if you end up with numbers of tiny ones (I was once tasked with weeding a mat of woolly thyme some yards across using a dinner fork - it was peppered with sedges probably mostly less than 1 in. tall and other micro-weeds).

The Irish moss on the other hand wants a fertile and moist soil, may go brown here and there if conditions are not soft enough for it. And is apt to need periodic lifting, division and replanting even when doing well. In part because it tends to mound up.

If not really inclined to engage in the upkeep that small alpine garden style plantings like these require you might be better off sweeping rock dust into the spaces between your pavers and leaving it at that.

Sedum 'Acre' works for me. It blooms in June and is very adaptable.

PS, I am deliberately allowing those off-shoots to grow in the gravel path because I will transplant them later to fill in another part of this project I'm not finished with yet.

Hey all thanks for all the wonderful comments. I’m debating what one poster said about just sweeping in rock dust or some small pebble material. He idea of a live crawling plant is appealing, but I hate to wait years for it to fill in, being uncertain of whether it will fill in small cracks, and movingthe pavers farther apart and Not getting good results.

If you find a garden center that sells the Irish or Scotch moss you can get about 30 or 40 small plants to pull apart for tucking between the pavers. Very economical and they grow pretty fast.

If you want moss between your pavers, find the kind you like, grind some up and put it in a squirrel bottle with water. Spray it between the pavers and it will grow quickly. I learned this from Martha Stewart and sprayed some large rocks that sit at the entrance to a path in my woods. I love how it turned out. I also let the moss grow between sections of concrete on my driveway. It's so pretty and keeps weeds from growing in those spaces. I'm definitely team moss ;)

OP (5 years ago) was asking about Irish 'moss'. This is an unhelpful common name used for Sagina subulata, not a true moss at all.