No it does not. If you look at the MIDI In/Out jacks on the Flextone III XL, they are 5-pin standard MIDI jacks.
From my experience in the past, the only devices that had the power-via-MIDI port capability were ones that had 7-pin MIDI jacks. One of the devices that comes to mind is the ADA MP-1 programmable MIDI preamp and it's corresponding footswitch. Also I remember that the GCX/Ground Control from the 1990's utilized a more-than-5 pin MIDI scheme to supply power to the Ground Control from the rack mounted switching system.
In short, that capability is not available with the Flextone III XL.