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Yes, you will most likely have to remove it to repair it. Just to be clear, you are talking about the quarter-dome shaped plastic piece that has the little cabinet, the speakers, and possibly the control center built into it, right?
This piece is made of ABS plastic, and will be quite brittle now that it is 40 years old. Removal is a two or three person job to keep the damage from getting any worse. You will struggle to find a glue that will stick to the old ABS. I have tried plastic welding, and have tried using the solvent based cements that are used in plumbing, but I didn't have much luck.
The bathroom components are made of the same stuff. I practically rebuilt by bathtub using epoxy based fiberglass laid up on the back surface--I suspect this is the surest bet for your repair as well. Don't try using the cheap polyester based fiberglass stuff you can get at the autoparts store--it won't stick.
If you only want to achieve a purely superficial fix, you might be able to squirt a flexible caulk into the crack, wipe it flat, and call it good. Not what I would call a structural repair, and the crack is likely to resurface eventually, but this would not require you to remove the piece.