Originally Posted by T-Mar

You'll never know until you try. You can get a rough idea based on the current lateral clearance between the stay and the chain, when it's on the small cog. If it's more than 5mm laterally, with your 6 speed set-up, it should work without need for spacers on 7 speed. However, most home mechanics neglect to consider that the chain moves vertically when derailing and shifting onto or off the small cog. They put the chain onto the small cog and install the wheel. Everything fits fine but the first time that they try to shift, the chain jams into the seat stay. You need the lateral clearance at a point above the small cog, so there's room for the chain to move vertically and clear the teeth of the cog when derailing. How high this clearance must extend depends on the size of the tooth jump between the smallest and 2nd smallest cog.