As a rule, there are only 3 non overlapping channels in 802.11bg (2.4Ghz). Those are 1 6 and 11
When you have AP on channel 1 and a 2nd ap on channel 3, they MAY be far enough appart such that they will not interfere with each other, but you should aways attempt to use the 1 6 11 seperation.
Note: The 2 APs will not stop the other from working, but will mean you get less effective bandwidth on both APs.
In short, 2 APs on channel 1 and 2 will end up working like 1 AP with all the clients on that.
Is it true that with at least some 802.11 protocols, two AP's using the same channel will try to equitably share the channel? Whereas, if they were on adjacent channels they'd simply see each other as noise?
I've not been able to find definitive information on this, but I have seen it mentioned on a number of reasonably authoritative sites. It's particularly an issue in Europe where the extra channels means that beside the "American" 1/6/11 channel allocation, you often come across 1/5/9/13, giving frequent 5/6 clashes.
When 2 Devices (peer-peer or AP-Client) are using the same channel then the 801.11 protocol means they will share in a friendly way. If, for example, you put in 2 APs at home and the same channel, then the effective throughput will be the same if they were all on the one single AP. To get better through put the APs should be on different non-overlapping channels.
Based on what I have seen, if the signal was strong enough, then channel 3-4 may "share" with some errors, but 3-5 would be moe like noise. But remember you dont even want to share if you can avoid it. So the 1-6-11 is the best bet. If you have to overlap a channel in use, then you would be better to put on the same channel so that they will try to play nice with each other.
I think the 1/5/9 would work OK as long as the signals where low enough. (ie: APs spread apart)