A very interesting question, and I admit to not really having a clue!
When I look at my Hessian Jaeger, the barrel is so thick for its length (i.e. extremely rigid) and the wood of the forestock is so thin, that there is no doubt that the wood is hanging on the barrel with no forcing affect. Probably, removing the forend would make no noticeable difference to the accuracy, but I'm not going to carve it up for the sake of an experiment!
However, looking at the American long rifles, the barrels are both longer and thinner, making them more "whippy", so the forestock may well have a complex effect on the barrel movement, such as dampening out certain vibrations and, of course, affecting the aim if the wood is warped.
In the case of muskets, the barrel is basically a tube of very large diameter, so it will also be very rigid. And the smooth-bore accuracy is so limited that the effect of wood/no wood will probably be undectable. Shotguns usually had a rather short forestock and basically a musket is like a shotgun firing a single piece of shot!
In short, the answer is yes/no/maybe!