Recommended course of action.
1. book massage appointment
2. dine
3. shower
4. massage
Note, the massage treatment at the arrivals MB Spa differs from those available at departures. I have found the massage at arrivals to be much more intensive and invigorating. Also your body position is more upright - you kneel into the chair whilst the masseuse does his worst to shift those knots.
Oh, there are a several internet enabled PC's just outside the Spa suite should you need to kill some time. Also, in case you're wondering, you can check your luggage in at the lounge reception as you arrive.