For an HDD: kinda. Spinning up and spinning down the disk technically always comes with the risk of the drive damaging because of the physical components involved, and will eventually wear out. Constant writes would definitely be far harder on it, but more spinning time is always generally likely to wear it out faster.
Constant reads wouldn't be as hard on the drive, but again, the more the mechanics inside the drive work/move, the more they will wear down. For HDDs, most failures are mechanical failures.
That said, even with a consumer grade drive, I personally wouldn't worry too much about it; modern drives are pretty solid in general, just make sure you backup anything important.
If you're really worried about it, WD's gold line is made for constant reads/writes 24/7 and to be reliable under those conditions