Thats a big stick.
If its not leakin now its not into the interior of the tire. Pull it out before you do a lot of work with it and it gets worked through and starts leaking.
Oh and I think I know what you mean by not knowing the construction of the tire. The tread portion of the tire is solid. On the inside it is a smooth surface(more or less, there are slight depressions where the tread is)