No Darren, this is not possible, if you are handy with the spanners, you can get the broken part of the key out and order a new key from FIAT and then it just needs to be coded into the cars immobiliser system.
The keys are coded to individual cars, and are not transferrable without transferring the injection ecu, lock set, and body computer. Also the body computer has to be of the same specification and have the same options as the original one or some items wont work.
Bottom cowling off, ign switch electrics and ariel disconnected, ign switch shear bolts out, insert remaining portion of key in barrel, tap barrel to reposition broken section (hold key downwards) turn ign to MAR, press in release button on side of switch, slide out barrel and using a pick or bit of welding rod push in rear of barrel, push remains of key blade out of barrel. Refit all parts except ign barrel. Order key from dealer. When it comes, (two days normally) check key fits barrel and when confirmed ok refit barrel and start car using new key but holding original key handle in the middle of the transponder ariel. Drive to dealer for coding. Refit lower cowling, job done.