I've had a Zippo that I use all the time for my pipe. I left the Zippo pipe insert in it for a good while. The only thing I ever noticed was a faint taste as I drew the flame in to light up, but if was gone as soon as the flame was gone. I eventually got tired of the fuel loss and decided to purchase a Thunderbird pipe insert for it that uses butane and produces a soft flame. It works like a champ, has a lifetime warranty, and the Zippo itself has all of its respective perks.
Just a thought incase the inner tube idea doesn't pan out to conserve fuel.