Your question really has nothing to do with IAG buying BMI, as it could equally be asked now for any T5-T3 connection.

There's at least one scenario that I can think of where it would be a problem. The devil, as always, is in the detail. If your nationality means you require a visa in order to clear immigration for the purpose of transit, but you would not require a visa to do a direct airside transit, then this plan might not work.