Nah mate! My ST passed it's MOT with no speedo.
They don't ride it, they just prod it about and check for loose wheel bearings and head bearings, loose exhausts and other bits falling off. Then they check your brakes, and that all the lights are working and aligned and that's about it.
They won't know the speedo ain't working just pushing it into the workshop.
I've got a spare speedo drive if you want one though. It cost me a tenner so it's yours for the same + postage if you need it.