And if they can, should they be able to?

Yes. And yes they should. Think about it this way, they aren't behind manacled behind the back like you see on cops or anything, they're just being slapped on whilst the criminal still has his hands out in front of them. Now a mage's hand gestures while casting have to be percise and the manacles don't allow this kind of percision to occur, thus, no casting.
A warrior on the other hand doesn't have to look pretty while hes spinning his spear or whirling his axe or chopping with his polearm so when hes all manacled up he can still do these things, but they're going to be rather clumsy (Ie. the -dex from manacles)

nt

Hmm... wouldn't there be considered some spells able to be gestured than others? Why not a simple first-tier spells thing being able to be used at less of a chance? Or allow spell-casting with a great reduction in success? A warrior can still function as well as any empowered character. Why the fussiness against mage criminals?