The only Logitech mouse that uses Bluetooth is the MX900. The one that comes with a USB receiver is not Bluetooth, it's a Logitech technology called "FastRF," their own variation of the standard-issue radio frequency wireless operation that's used by 95% of wireless mice. Bluetooth mice are still very rare and expensive, most likely because Bluetooth isn't very well suited to mice. Its data rate is poor and it can't keep up with fast mouse movements.
There's nothing wrong with your typical wireless mouse though. Bluetooth has the convenience factor of not requiring any kind of USB connector on the computer, and it can also be used to sync certain cell phones and PDAs. Other than those, Bluetooth has no advantages and plenty of drawbacks. Most Bluetooth mice are very expensive, and many don't work well.
I don't think a corded mouse would draw much power from the battery. The amount of power necessary to run a single red LED is very low, and recording mouse clicks and tracking is pretty low too. My Logitech MX700 cordless mouse, for instance, takes about a week to completely drain a pair of AA batteries, and this is for a mouse with a very advanced optical sensor and a bunch of different buttons.
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