Simple answer: Yes, but the speed at which your card wears will vary greatly depending on brand, clock speeds, undervolting, and other factors. In general, you shouldn’t expect your card to fail before its warranty is up, but on the off chance that it does, you’ll be lucky enough to get a free replacement.
Generally speaking, people using modern graphics cards (like the latest RX 470, 480, and 580s) will be able to get a few years out of them running 24/7 before experiencing total failure. Some have been able to get 6 or more years out of a modern card. Before that time, however, many will see their cards’ fans die and need replacing. Thankfully, that’s a relatively easy fix.
To ensure that you get the most time out of your cards (and therefore the most profit from your rig), it’s best to make sure you do a proper undervolt of your card to get its heat and overall power draw down to minimal levels. You’ll be giving your card less power, and you’ll get the same or better performance.