No, you can use lenses designed for a larger sensor (or film size - ie, 35mm film or full frame sensor which are essentially the same size) with a camera with a smaller sensor assuming you can make it work with the sensor location relative to the lens mount (and again, using a lens designed for 35mm or full frame tends to work with m43 or Nex). But a lens designed for a smaller sensor (m43) will not work on a camera with a larger sensor (Nex) because the lens was designed to deliver light only to that smaller sensor. Which is why m43 lenses can be a good deal smaller than Nex lenses of a similar focal length. So, no, you can't use an m43 lens on a Nex - as Nic says, it'll only provide light to part of the sensor.
Don't bail on your GF1 just because a lot of us are having a great time with a Nex. Shooter is the kind of guy who LIVES with one focal length and INHABITS it and makes it his own. The Nex is good for that if you like the focal lengths they have available at the moment. I love the Nex in addition to my m43 gear, but I love having a variety of lenses, including long ones. And the Nex doesn't have 'em and even when it get's em any long lenses are going to necessarily be silly large for such a small camera (again with the bigger vs smaller sensor thing). My m43 kit is the heart of my system and I envision it being so for the foreseeable future. The Nex is a wonderful camera for some types of shooting but, for me at least, about 95% of what I love about it is the flip up screen that allows me to shoot from the waist or belly very discreetly. If Olympus or Panasonic comes out with a small camera with an equally good and useful screen, I'll happily sell the Nex and just use m43.
I don't want to talk you out of a Nex too, if you can afford it. Its a great camera. It's just not a 'system' camera yet and will probably never be as good a system as m43 just based on lens size. But its an absolute blast to shoot with. And the Nex 3s are being discontinued so they're starting to come down in price pretty rapidly. Same exact camera as the Nex 5 in terms of taking stills too - just a slightly different shape and it doesn't work with a wireless remote. But definitely worth a try if you can swing it.
Anyway, happy to help clarify matters, even if it ends up confusing you more!