Can I use an inner tube that's too narrow for the tyre?
In my experience smaller ones go in fine and last as per normal (not that I have pushed this to extremes with a 700x20 in a 700x40 but I only have 26x1.5 MTB tubes and they work fine in 26x2.00 tyres).

Allegedly putting a smaller tube in the tyre becomes a problem if and when you repair it, the patch doesn't necessarily stretch with the inner tube and it can come off.