[MAP-3120] Do I need to install a Mobile IP server for MAP-3120 - the Layer 2 Mesh Access Point, when I have a need to provide the mobility around the MAP-3120 covered wireless area?

No. There is no need to have a Mobile IP server for MAP-3120.

The MAP-3120 is a layer 2 bridge that with dual RF interfaces bridging in between.
The bridging algorithm is base on layer 2 MAC address. So, it is protocol independent device that always follow layer 2 MAC address to forward or not forward the packets between the two interfaces (Interface of LAN/WiFi and interface of backhaul).

Whenever the mobile worker change to another MAP-3120 and this MAP-3120 learned about this new client (new MAC address), then it will start to forward packets to the destinations.