I’d assume that he’d be able to play, yeah, even with limited arm movement
Boccia is a very inclusive sport. I know not the same thing, but you can even play it if your visually impaired.
For example, in visually impaired boccia, a scaled down boccia grid is used. Grids are scaled down versions of the court, and different shapes and sizes of pegs are used to differentiate between the two colours.
Is he able to grip things? If not, he might need a little bit of help from someone, who will place the ball in his hand and help him get a firm grip of it. Not sure how limited you mean, as in what he can do with his arms, but I highly suggest using a ramp if the mobility in his arms won’t let him toss the ball far (based off of what I heard, I’m assuming this would be suitable for him)