I had something similar happen to me recently...I got a compression tester stuck in the spark plug hole and it wouldn't come out. Then the hose broke off, so we tried pounding a socket into the whole. That got stuck, so I had to remove the head and get a machinist to get it out. Kind of sucked since it was such a routine check and it ended up costing me over 12 hours of labor to get my car running again.

Anyways...I wouldn't run the engine without removing it first. It may get dislodged and screw everything up. I think removing the cylinder head is the only way you can get to it. Removing the oil pan probably won't help but I would try first since that is much easier to do. Yeah, taking off the head sucks but it is valuable knowledge to have and I wouldn't risk totally wrecking the engine because of it.