hmm, that's very interesting and no I don't think so -- sounds like what you may be alluding to is setting up a topology, there is a cluster tolerance you can set up there. Not sure about any licensing restrictions if any - if you have ArcInfo (or Advanced, as it is now called), then no worries.
Here's the thing though - setting up a topology requires import into a gdb feature dataset and is potentially a bit time-consuming to initially process and set up the rules. Plus, I don't fully know your situation and while using a topology is most effective for some workflows, it can be overkill and bog down other workflows....have to use your judgement.
Could be all you want to do is execute Integrate (but make sure you make a backup copy of the dataset 1st). Results will vary and you may be unpleasantly surprised...no need to go on about that, you can imagine I'm sure. I think of Integrate as sometimes an expedient means to 'slam stuff' together without the validation a topology would enforce. It is shooting from the hip, so exercise care (copy the dataset and experiment) and define a close (small) measure of tolerance...
One more thing, since you've got me babbling -- I once had points (fire hydrants, I think) collected so that, as you describe, were sometimes very nearly coincident, but the 'slam together' approach was no good -- I need to identify the dups. So what I did was run a small Buffer with dissolved overlaps to 'enclose' the duplicate candidates. What that did was to enable me to very quickly select the dissolved buffer areas that were not 'round' thus larger in area. Area is a criteria I can select, export, and provide a report to someone needing to 'see' both (or more in some instances) candidates to figure out what is going on and how to then assimilate the data into the single shapes they should be. Yes, so that's Buffer in proximity analysis.
Hope that helps.
-Wayne
