Nick,
Your MEIR will still be valid and 'yes' you can quite happily excersise the privilages of the MEIR until Sept(if thats when it expires). HOWEVER....if your MEP rating expires in May then you cannot obviously fly an MEP aircraft...catach 22! You could however excersise your MEIR on an SEP...assuming of course your SEP rating is current.
To keep it simple....you presumably have 3 ratings on your licence - SEP, MEP, and MEIR. Only the MEIR needs to be current for your TR course. Clear as mud eh!!