If i factory reset my iPhone will it relock to O2?

I've had my iPhone 3G for a couple of years and when out of contract i asked O2 to unlock it, which they did. I've used a Three sim card and it works okay. I've now decided to sell it but before I send it to the buyer i want to factory reset the phone. Will it remain available to use on any network once i've reset it, because i've advertised it as an unlocked phone?

Also, just as a side note if you can help. Its running iOS 3.1.3. Once factory reset and connected to iTunes will it force an iOS 4 update or can you choose not to update the OS?