Woofer and subwoofer are different things.
A woofer in a speaker is also tuned and crossed-over specifically in its design.
And, I'm not saying it is the wrong thing to do, just that it is usually not the best situation. It is not about the sub being close to the speaker, it is about the best position for the sub....which usually isn't where the speaker is.
Depending on the subwoofer, isolation pads may not do the trick. I have seem some subs that a rock solid with little or no vibration, and others that could move across the floor.
