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I don't think it should be a problem. I keep a Velcro strap around my XR650L on the brake while on the center stand to keep the kids from accidentally knocking the bike forward off the stand. It sits like that for months at a time with no problem.
Haven't seen that before. What is it called?
Shouldn't be a problem with having the brake engaged for a long period that I can think of. Some racers do that the night before a race as it can help with brake feel.