There is a slight gap in the overhead wiring between the Liverpool South Parkway area & the Old Trafford area. Unless you are proposing routing the services via Chat Moss
But a BEMU service on the Lime St-Oxford Road stopper looks feasible with the TPE-specced units.
The wiring gap on the CLC route is 25 miles from Liverpool South Parkway to Trafford Park West Jn, and there is charging under the wires at both ends (though finding somewhere to pan-up east of Trafford Park might be tricky).
After charging via Oxford Road, such trains could also reach, say, Buxton on the 17-mile gap from Hazel Grove.
I could easily see Northern (or DfT/DfTO) adding to the TPE order for some of its BEMU requirement.
However, it seems to want a DMU/EMU/BEMU platform with conversion options for each, which the Adessia doesn't address.