Without wanting to put words into Sunnyjim's mouth, what he really meant was "it might" rather than "it will".
Driving gives a different perspective of using the roads and perhaps provides some empathy from what drivers see etc. It certainly doesn't naturally flow that it will make you a better cyclist (or vice versa) as that depends upon your own personal circumstances.
There are a lot of folk who are poor drivers and poor cyclists (not necessarily mutually exclusive). Some of these may benefit from learning the other skill, many won't (either they don't have the ability to or don't want to).
Thank you 400bhp - That's indeed what I should have said.
Judging from the behaviour of some driving instructors, driving lessons only might make the OP a better driver.