It is possible that the USB device plugged in the host computer is seen by the host computer as a kind of mouse or keyboard. As such, this would make the computer ready to accept mouse-like or keyboard-like events (as if someone was clicking or typing text).
It is conceivable that the USB device is itself ready to receive and process keyboard-like event. The clicker will not send those, of course; but Logitech also manufactures wireless keyboards and it would make sense that they reuse components between products, to save on development and production costs.
Take this two together, and you have it: possibly, you just gave any attacker a keyboard to your machine. At that point, many things are possible...
Hopefully, the clicker and the receiver have some sort of automatic cryptographic pairing procedure which reduces the possibilities of an hostile hijack (a man-in-the-middle could still be possible, since avoiding it may entail substantial computing effort from the involved devices). However, since this communication is between a Logitech device and another Logitech device, and the two of them are sold together, then there is no incentive for this protocol to be standard or at least documented. So you cannot be sure that things were done properly.
Also, any wireless receiver implies that there must be some driver software which analyzes data obtain from "the outside". Any bug in such a driver could be exploited (and yield kernel-level access to the host computer).
To sum up: yeah, there are conceivable risks for the host computer.