When casette hubs were first introduced in early to mid 1980's, 6-speed was still state of the art so that is what the first casette hubs had. By 1989, 7 and 8 speed was much more prevelant on high-end bikes so it is unlikely that a bike manufacturer would spec a casette hub (indicating a decent quality bike) with only 6 speed. If your 1989 bike is a 6 speed, it was probably a lower end economy model that still used a freewheel to keep cost down.
Assuming the frame is 126mm width (safe assumption for a 1989), then yes a 7 speed freewheel can directly replace the 6-speed freewheel and it will work fine friction shifting. If you have 6-speed index shifting you would at minimum need 7 speed shifters to preserve the indexing with the new FW.