No my mistake, I thought you were unplugging the audio connections (jackplugs).
Yes, using a 2-pin mains (AC) plug can make a difference as it doesn’t have an earth pin which 3-pin plugs have.
Earth (a.k.a. “ground”) connections (or lack of them) can be a source of mains hum …
Low current wiring is particularly susceptible to ground loops. If two pieces of audio equipment are plugged into different power outlets, there will often be a difference in their respective ground potentials. If a signal is passed from one to the other via an audio connection with the ground wire intact, this potential difference causes a spurious current through the cables, creating an audible buzz at the AC mains base frequency (50 or 60 Hz) and the harmonics thereof (120 Hz, 240 Hz, and so on), called mains hum.
A floating ground circuit is a circuit in which the ground is not used … not connected to a grounding point [> e.g. 2-pin mains plug> ]. Ground loops can form when equipment with floating grounds are connected to properly grounded equipment [> e.g. 3- pin mains plug> ], and results in a current traveling between the two devices.
If you are using any outboard (externally powered) audio hardware, make sure all the equipment is plugged into the same power strip. Grounding issues can cause ground loops, which will appear in your recording as a hum.
NB: the earth (ground) connection is a safety feature, do not disconnect it.