Can you use a USB Wireless mouse with an iPad through the lightning to USB adapter?
Yes, it should definitely be possible - and it should work with the same functionality as a Bluetooth mouse.

The Logitech unifying receiver presents itself to the operating system essentially the same way a cabled mouse does. Therefore iOS works for that receiver without extra "drivers" or anything like that.

I have personally used a Logitech wireless mouse with an iPad before, but I can't say if it is the same exact model of mouse, you have. You might experience that extra buttons for example have no function or similar, but the basics of pointing and clicking should work.