I don't doubt that you can physically carry big enough of a payload on an intercept trajectory, I just doubt that a clandestinely manufactured quadcopter will be able to either autonomously track its target (not big enough to carry a radar) or be controllable from 20 miles away (even in Ukraine EW is pervasive).
More realistically they'd try to modify the targeting of their existing AtoA and send fighters. Which is kinda like a bunch of big drones carrying small ones.
Fighters and AtoA are extremely expensive and difficult to manufacture in quantity. You can make drones pretty much anywhere (with a steady supply of cheap flight controllers), for next to nothing, and strap all sorts of payloads to them. If I were the adversary, I'd send a bunch of cheap drones first, to deplete defensive ammo, and then _maybe_ send something heavy duty and expensive. Literally, one single rocket (not to mention a fighter jet) can cost as much as a couple hundred disposable drones. You tell me which is harder to defend against, one rocket or a huge swarm of semi-autonomous drones (computer vision in the terminal phase is quite common by now).