Yes, you can donate blood while taking Plaquenil. (Always check with the center where you donate about restrictions on anything you're taking!).
I agree with North that you have to decide whether you are up to donating on a particular occasion. I skipped several times because I just felt under the weather, and figured that I didn't need another reason to be a little more tired.
But I do disagree with North about the AS-related diseases being possibly transmissible via blood. My blood center (Blood Center of Wisconsin, based in Milwaukee) is on the forefront of research for such things, and I am certain that if there were any even theoretic concern that they would turn down my donation.
I took Plaquenil for 2 years. The only side effect I had was significant sun sensitivity - and it seemed to help reduce my flares. I'm off it now because my current rheumy has tentatively un-diagnosed my USpa
Best of luck to you.