I didn't know, so I figured I'd give it a shot. I brought an ancient and non-functioning 1987 Macintosh Plus 1MB to the Apple Store in the Meatpacking District in NYC, and this is what happened.
Overall, they were surprisingly unfazed by my request for repairs. They were impressed that I had it, and seemed genuinely interested in helping me get it fixed. They couldn't do anything for me, since Apple only keeps equipment from the last five years on hand, but they pointed me towards Tekserve, another Apple-centric store in NYC.
Thanks to Nick McGlynn and Gawker.tv for shooting the hidden camera footage!