you must determine the axle spacing to see if a different freewheel could be used.
If your 6 spd is an ultra-narrow model to fit a 5 spd hub (120mm), then no, you can't use a 7 spd.
If your 6 spd is a standard width 6 spd freewheel, then the hub is also a 6 spd hub (126mm).
yes, an ultra-narrow 7 spd freewheel will fit.