I'm guessing that the "battery" in the pen will be a supercapacitor. Batteries don't charge that fast. But at least supercapacitors don't wear out with age. (Meaning that if the phone is still working 10 years from now, and on its 3rd or 4th battery, the pen will still be on the original supercapacitor.)
Using Bluetooth, though, even low-power Bluetooth, is going to eat battery - and that will come from the phone's battery when the pen recharges.
So all that's really added is the different things you can set it to do with different clicks. And you should still get at least 2 security updates a year for 2 years. Not enough to make me want to give up my Pixel 2.