Afraid not, it only charges the battery pack, for the controller does not send the signal down it.
You can get an adapter so that your controller will work on PC even though it is wireless, its pricey though.
$15-20 isn’t really pricey, especially since it lets you connect up to four controllers. The only problem is that you have to unplug your 360 if it’s in the same room so your controller doesn’t try to connect to it instead.
It’s also worth mentioning that in my opinion a 360 controller is the best gamepad to use on a PC. I don’t even own a 360 and I have one. It just…works.
that d-pad is horrendous tho…