You can use EDMX and code mapping together only if you have separate context type for each approach (you cannot mix approaches in single context type). That is probably the biggest disadvantage because it leads to more complex code and maintenance.
For example if you need to have some entity in both contexts types to use it with both new and legacy code you must maintain its mapping twice. You must also be very careful about not duplicating entity class itself = your code first must use class generated by custom tool for EDMX but this will not be possible if they are not using POCOs in current solution.
Another problem will be database integrity. If you will need to save changes to both context types in single transaction you will have to use TransactionScope
and distributed transaction = MSDTC (each context instance will handle its own database connection).
If you are sure that whole system will be migrated you can probably think about using code first instead of EDMX (but be aware that code first mapping and DbContext generally offers more limited feature set). If you are not sure that you will be able to complete whole migration don't even think about using code first because leaving system in the state where half uses code first and half EDMX will make everything only worse and much more horrible.
Being sure is little bit theoretical because in SW development the only think you can be sure about is that requirements / situation will change. It means that migration should be very carefully considered.