The biggest thing it will cause is noise. It may also leak in some outside air, but I think more likely it will leak exhaust gas out. There are some high temperature tapes that are available as a temporary band-aid, but the best bet is a used unit from a boneyard.
If you can't find one, a good muffler shop should be able to bend and flare some tubing to match the factory part. It doesn't have to do the bends exactly, but would need to have the flare fittings.
Good luck getting the old one off.........
tom