Definately, that's largely how our local museum got started. You don't have to outright donate the object, most museums have a lone policy for a given term. I would check out their policy though, sometimes if you don't retrieve or renew the loan the item may become the property of the museum. Also most smaller museums don't have insurance (i.e. the budget).
Yep. Last April I helped a local group in an effort to positively identify the crash site of a B-24 Bomber that went down on a training mission. I found several items, as did others in the group. My best find was a brass plate that was once attached to an instrumentation rack. Had the mfg name, part number and serial number clearly visible. We all donated our better finds to the local museum, and this June they will be opening an exhibit to the public. The finds that didn't have value in terms of helping identify the aircraft were grouped together and re-buried at the crash site. Seemed like the right thing to do honor the memories of several airmen who lost their lives in the crash.