When you spin a sample you make sure that orientation effects are averaged faster than the relaxation time. This holds true if you spin a sample at 8 s^-1 and H1 relaxes at 1 s^-1. Now, wobbling (aka shaking) will keep orientation of the molecules for the most part (unless it creates spinning motion in the solution). It will change several %, but the general direction will be the same. So, no, shaking will not do the molecule averaging like spinning does.
Btw, why do we spin samples. I mean, if the tube is half decent and you spend 5 minutes on shimming you get about as good of a result. All spinning does is hiding poor XY shims by averaging them.