I have brought my Bike Friday into many hotels and never had a problem, though I often expected one. Other guests are either oblivious or curious. Employees never said a word. I do agree you might be best off not even asking. Worst case, they might make you check it in the lobby.
I would not be too concerned about leaving it in the room. Only the maid is likely to be in the room, and there are probably cameras in the hallway.