Hi Timothy,
In terms of the entire product, going from 6.1 to 6.3.2 you'd need an interim upgrade of 6.2.2 between them.
Technically they aren't compatible though what you're asking here *might* work, but no guarantees as its not been tested. Nobody would have a comparison of changes in the LE code between 6.1 and 6.3.2 releases.
I'd give it a shot and try the nhExportLiveExCfg and then nhImportLiveExCfg commands to see what results look like.
My guess is that it won't fail outright. That you'll either end up with 100% success, or a partial success with some minor config items on the new system that will need to be updated or reset.
Hope that helps.
Thanks,
Michael