It seems more likely that Russia would just be using the hardware to communicate with their own systems, probably not Starlink's actual network. For a kamikaze drone, if you don't have to pay for the antenna, great, money saved. Two years ago there was a Black Hat talk on hacking the equipment, full compromise, is it inconceivable that Russia could find more vulnerabilities? They have their own satellites, too, it's not like they need to use Starlink unlike Ukraine.

I dont think starlink antena is able to communicate with their own satelites - those are much higher and you would need much more powerfull antenna.