Performance impact of adding a foreign key to a 1M rows table
You are far better off maintaining a foreign key (FK) constraint if your data warrants it. 

MySQL will automatically create an index - the FK must reference a UNIQUE KEY (obviously, can be the PRIMARY KEY (PK) - from here). 

See here for a host of reasons to as to why applying data constraints in the database is a VERY good idea. The index on the T table will increase lookup speed at the price of a small hit for inserts. 

Believe me, you will save yourself an immense amount of grief by making use of the database capabilities rather than trying to do this yourself.