I bought tires in 1992, rode a bit, put my bike away, rode again in 2001-2002, put my bike away, and started again in 2013. The tires held air, and I actually took a number of rides on them, but some days they were flat for no apparent reason. One day I had to walk home, and I found walking while pushing a bike with a flat tire took a lot more energy than just walking.
Flats are really inconvenient. What if you flat many miles from home? Why put yourself through that?
My reco is to buy new tires and tubes. Some shops will mount them for you at no extra charge if you buy them at the shop. If they charge for mounting them, I recommend you invest in a Kool-Stop Tire Jack and a good pump and mount them yourself. You'll need the pump anyway.