Absolutely!
In this sense, think of your remote workers as you would a regular office employee: when you hire someone full-time, they work for you on a set schedule of 40+ hours a week for most of the year to help your business grow. The only difference is that remote workers work from home.
Therefore, we strongly recommend that you offer your remote workers the same number of sick days and vacation days as your other employees and that they follow the same rules for taking time off.