Yes, just check it out and run it. If it was running 5-6 years ago there is no reason it shouldn't run now. The rings could be stuck and give variable compression readings, but it will free up after a couple hundred miles of running. Make sure you drain the gas tank then pull and CLEAN it. Old gas leaves a residue which new gas (especially with ethanol in it) dissolves. The residue gets in the engine and gums up carbs/injectors and even valves. I've had it get into valve guides and cause the valves to stick open and bend pushrods. I've brought many old engines back to life after sitting for years -- you should have no real problems. Pull the fuel line and stick it in a gallon anti-freeze jug (or similar) with fuel in it for temporary running -- until you get the tank pulled and cleaned. Can't go far, but can run it enough to see what condition it's in and run around the block a few times.
The flexplate isn't a big mystery. I've ripped the center out of one on a little 195.6 Rambler six cylinder. Flexplates are a hardened steel, and get brittle with use and age. Cracks usually develop around the bolt holes first, either at the crank (most common, that's where most of the stress is) or where the converter bolts on. The bolts may have not been tightened properly causing excess stress, could have just been age, or the metal may not have been properly hardened.
Engine balance wouldn't affect the flexplate -- that would affect the crank bearings. A bad torque converter can put excessive stress on the flexplate though. A bad bearing in the converter can throw the converter out of balance enough to stress the flexplate, but the harmonic balancer or crank balance shouldn't.