In theory yes but in practice backlash and stiction make drive currents much less useful than the raw force at point of contact for any realistic gearing. And an important part of weight estimation is that force lateral to the point of contact. Now, your arm motors will be drawing more current as they move so again in theory you can distinguish that, you've still got the weight of the whole gripper added in.
I spent years of my professional life on these topics[1] and from my experience motor drive current usually isn't enough to narrow down the weight of an object in a typical picking task even to within a factor of 2 to detect when you've accidentally picked up two items from a bin instead of one.
I spent years of my professional life on these topics[1] and from my experience motor drive current usually isn't enough to narrow down the weight of an object in a typical picking task even to within a factor of 2 to detect when you've accidentally picked up two items from a bin instead of one.
[1]https://patents.google.com/patent/US12612266