Joined: Jan 2010
Posts: 9,835
Likes: 1,816
From: Northern California
Bikes: Cheltenham-Pedersen racer, Boulder F/S Paris-Roubaix, Varsity racer, '52 Christophe, '62 Continental, '92 Merckx, '75 Limongi, '76 Presto, '72 Gitane SC, '71 Schwinn SS, etc.
People use 7-speed cassettes/freewheels with 8-speed shifters all the time, and the shifting is acceptable for most.
I have even raced on such a setup for many years.
What WASN'T done in this case was to back out the B-tension screw to match the smaller freewheel.
The enormous chain gap that resulted from the smaller cogs made the derailer's motions very ineffective at moving the chain from one sprocket to the next.
One more consideration would be if the 7-speed freewheel was truly index-compatible, but the B-tension screw still needs to be set with the top pulley close to the sprockets in any case.