Balancing gunked up wheels

Last month I had my studded snow tires mounted and balanced on a spare set of aluminum rims so that I could change over when I was ready. Afterward I noticed they were very gunked up with brake dust and grease so I cleaned them. Now that I've degreased them should I have them re-balanced?
Also, what kinds of mechanical problems can driving on unbalanced wheels cause? Does this put undue wear and tear on the vehicle?

You would have to have a lot of gunk on a wheel to make any difference in the balance. It would be doubtful that you could have that much grease and dust built up on the wheels uless it was over 1/8" thick or something. I guess it is possible but it's not likely. Runnig with badly out of balance wheels can take its toll on wheel bearings and suspension bushings but it takes a while to cause any damage.

Thank you very much for the info, the wheels in question are studded snow's from another vehicle. When I first put them on I noticed a slight vibration, but now after 200 miles they feel fine.