Does my Arduino-based device need FCC certification?
You are confusing certification and emissions requirements.  Only intentional radiators need to be certified.  From your description, your device is not a intentional radiator.

However, you are still obligated to ensure it does not radiate excessively.  The limits are defined in part 15 of the FCC rules.

How you determine for yourself and ensure that the device does not radiate more than allowed is up to you.  The FCC doesn't go looking at the millions of devices that are unintentional radiators and test them for compliance.  However, your competitors might.  If they find your device radiates illegally, they can file a complaint with the FCC.

The worst case is if some communication got interfered with, the FCC investigates, and finds one of your devices causing the problem.  Then it gets serious fast.

Large resellers may require a recognized lab to certify that your device radiates legally, or they won't carry it.

All that said, for a little guy selling a few 100 gizmos a year off some web site, there is very little chance anyone is going to check whether the device radiates within the limits.  If you follow best practices, like a good overall grounding strategy, filtering of external wires, etc, chances are very low your device will radiate enough past the limits for anyone to notice or to care.

As Dirty Harry would say: "you've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?"