Seafoam is a fuel additive, not an oil additive. So introducing it to your gas won't affect the clutch, nor will it likely address an oil burning. It is possible that some of you oil burning is related the piston rings, and if they are indeed crudded up, then Seafoam won't hurt a bit.
Oil additives should be avoided (unless it's a zinc-based product) unless they are specifically designed for wet clutch bikes. Before you tear into the clutch, you should do a thorough 3,000 Maintenance regimen on the bike, including lubricating the clutch cable (or replacing it) and adjusting the lifter nut. You'd be surprised how well a 50 year old motorcycle responds to some competent TLC.