As long as the plant is healthy, go for it. Harvesting for cooking, drying, or cuttings is good. Just know it may not grow back quite as fast, but you can give it a good haircut.

If it is a healthy plant, I would try layering. It is another propagation method that cuts a rooted twig from the mother plants after roots have been made. Google layering propagation.

FataMorgana

This year a few thyme clippings that were meant for compost ended up on the lavender propagation dirt and are taking very well considering they were just dying twigs. Thyme is hard to kill incidentally. Here in RI it I have creeping, culinary, and lemony thyme. It all grows like weed in clay soil. In pots they are most susceptible to freeze and drying. In the ground, not so.