Damage through thermactor hole?

I accidentally put too small of a plug in the thermactor/exhaust hole in the back of one of my heads, and instead of threading it just slid way in.

The top of the plug is about 1/2" in to the head.

Before I fish it out and potentially push it further, there's no way it could cause any damage if I lose it or it's stuck, right?

The thermactor port goes down to the bump in the roof of each exhaust port, but there's no way a 1/2" plug could get in to the exhaust port or cylinder through there, correct?

This is for the fuel injected 5.0 in my '67, which doesn't have the crossover pipe in back.

I generally know what I'm doing :) Apparently wasn't paying attention this time.

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