What is the bath made off?
if it is metal then probably, although I would add loads of old towels as padding.
Or cut 3-4 ply to sit on the edges with some kind of lip to stop it moving.
If your going to put a board over the bath, screw some 2x3 lengths onto the underside so they have the blanket between them and the sides, that ought to stop it sliding off.
To skim my Daughters bathroom ceiling I fixed lengths of 3x2 across the bath with double sided tape to stop them slipping and boarded on top so had a nice sturdy platform .
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