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No. InDesingn has never been backward compatible in that way, and at this point the only path back to CS2 is to export to .idml, open that in CS4 and export to .inx, and open that in CS3, exprt to .inx again, and open that one in CS2 (there's a hack for making CS4 .inix open in CS2 at http://indesignsecrets.com/double-downsave.php, but like all hacks it may not work).
If you didn't do anything in CS5.5 that is unsupported, and your file is reatively simple, it might make it throughthe conversions relatively intact, but there are significant differnces between text engins from version to version that will cause text to flow differently so you need to check carfully for changed line breaks and oversets.
Not a good one.
At least you need InDesign CS4 to do so. InDesign CS4 is the only version that can import IDML and export INX.
First you have to export your CS5.5 file to IDML (the InDesign exchange format). InDesign CS2 (or CS3) cannot open that. So you have to open that in InDesign CS4 and export from there to INX format. Problem now is that InDesign CS2 cannot open that either. But there is a workaround for this.
Keep in mind: for a regular workflow this is a desaster. Even for simple text composition. Too much changed since InDesign CS2.