Well yeah, IF the bearings are shot, true.
But I would start off by making sure you centre the disc on the platen as well as you can. Do this by cutting out a half circle of cardboard/very thin ply/w.h.y. to EXACTLY the dia of the platen, WITH a little extra "lever" left on one side. Then slip the cut out semi circle against the platen, half circle down, ease the abrasive disc over the cut out, between the front edge of the sanding table and ply/w.h.y. Then gently rotate the platen by hand, so that the sandwich of ply/cardboard/whatever and the abrasive disc sink below the level of the sanding table, lining all up the abrasive on the TOP edge of the platen carefully as you go. Then rotate a little, grab the "lever" to gently pull the cardboard/ply/whatever out of the sandwich, leaving the abrasive disc quite nicely lined up with the platen.
NOT spot on, but near enough, and certainly works for me, with no really noticeable vibrations - AND takes longer to write about than to do!
Does the sander vibrate WITHOUT a disc installed? If yes, then probably shot bearings. If not, try the above.
HTH