I have a question relating to a hypothetical scenario where BA has bought BMI and thus has more slots at LHR, but no space left at T5 and so adds destinations to other LHR terminals (3 for instance).

In such a scenario where BA switched its Orlando flight to LHR from LGW and I were travelling BA from BRU to MCO, arriving T5 (from BRU), departing T3 for MCO and my baggage was ticketed to final destination MCO, what would happen if I exited T5 via and took Heathrow Express to T3 and checked in there?

Would it be a problem or not?