It's normal for a worn engine to be overbored by .030". The maximum for a 350 block is usually .060", but there are aftermarket manufacturers such as World Products have small-blocks that accept up to .120" over.
Ken's right on the money, as a matter of fact, years ago, some of the serious 1/4 mile racers would bore a 327 cu. in. engine .120" over. As for the kind of HP it would make, that depends on a number of factors. Compression, cam, heads, intake, fuel source, blower, turbo etc. The HP goes up with the price, but longevity often goes down.