You can normally open CS3 files directly in CS6 Application. You don't need previous versions of Indesign. The problem is only in downsaving.
Anyway, before open them in Indesign CS6, I recommend a backup of all the files.
If you experience any problems in open CS3 files in Indesign CS6, It could depend on thirdy part plugin.
Direct conversion of CS3 to CS6 .indd can result in file problems later (not always, but sometimes you don't know until it's too late). Best practice, in my opinion is to exprt your CS3 files to .inx and open those in CS6. If that's not possible becasue you no longer have CS3, the next best thing is to open in CS6 and immediately export to .idml, open that and save witha new name so you don't overwrite the old file.