Yes AC, I have for years had cordless mice - logitech, biggest problems were:
1. the small glider feet, which it slides along on kept falling off
2. the old dust & dirt inside problem.
So for these reasons I got another logitech product called MX700 which is infra red. It has feet (gliders) that are recessed into it and is infra red, which cures problem 2.
You do end up with a charger unit/signal receiver on the desk, the delay your friend is concerned about is non existent IMHO, not having to clean the thing out is great and it moves consistently (glides).
I read a test on toms hardware guide prior to purchase and was convinced.
Now had it for just over a year and would buy same or newer model again.