MIDP's application model doesn't really specify whether you can have multiple MIDlets running simultaneously. It's up to the implementation. I believe my Nokia 3650 does allow MIDlets to run simultaneously, but I'm sure my Motorola i85s does not. At any rate, the specification doesn't guarantee that MIDlets can run simultaneously, so you can't count on it.
That being said, you may be able to achieve the functionality you're seeking regardless. MIDP 2.0 offers two features that may do what you want. The first feature is the ability to request that a MIDlet be run at a certain time. This is great for ticklers or appointment book applications.
The second feature is the push registry, which allows MIDlets to register interest in incoming network connections. When the phone receives such a connection (incoming SMS message, maybe) it launches your MIDlet and you get to handle the incoming connection.