Is it normal for a fan controler to have a Humm that you can notice when the fan
Is running or not ? 2 Year old Heil gas unit.

No this is not normal, if you touch relay can you feel the hum? In the off position?

In the process of purchasing the home and currently not in the area to check
Relay. The local Heat / Air company checked the unit, they installed 2 years ago,
And reported that this hum from the fan controller was normal.?

Some times a transformer will make a humming noise but that can be solved by tightening the screws attaching it or by replacing it. A relay will not normally hum if it is not energised (no power to it) whereas a transformer has power all the time. Good luck. Mike