Yeah, they will last several years. I still have an HD 5870 in one of my computers and it stays on 24/7 and overclocked 24/7. No issues at all. Once every 6 months or so, it's good to vacuum the dust out of it so it stays running as cool as possible, but that's about it.
Some friends of mine are still using some even older ATI 4000 series and Nvidia 8000 series GPUs. The worst that's ever happened is the fan died. $5-$10 for a replacement and it's like new again.