Not under load. Actually, I don't think it will shift period under a load--when I tried mine, it just would stay in gear, and then when I left off, it would go. I don't think you'll break anything trying to shift under load, but just let off a bit when you shift, then resume. Don't forget--you can shift at a full stop too. No need to be pedaling.

Have you oiled the hubs yet? I suspect they are dry, if they have been sitting for years (and it is possible the prior owners never would have oiled them either). I'd pop it off, and make sure the balls have oil in them, then pour something like a tablespoon of oil into the oil port.