I'm a little confused by what you mean by "running"? There is nothing actively running for fMMS except for when you have the GUI open or the push daemon has been activated by a notice from your carrier that a message has arrived.

By default when the push daemon gets info from the carrier about a new MMS message (via an SMS-like message), it stores that data in the fMMS database, and then (based on settings) may try to retrieve the data portion in the background. If you mean you don't want it downloading MMS in the background, jut change the network setting to polite. Then it will always ask before downloading. The push message itself (the SMS portion of the MMS) is sent by the carrier through, and there's no way to stop those, short of going off-line.

If you're talking about the audio message, I'm pretty sure that's handled at the system level for sounds and what not. There's no way to stop fMMS (or most message providers) from triggering the system to tell it that it got a new message. Though you can put the device on silent mode, or use an app like led pattern changer to change the pattern and/or response for each message by type.

If neither of those addressed what you're trying to do, please be more specific on what exactly you want "disabled". It may be fMMS could use one more feature if there's enough people that want it.