This is of course correct but there is an added feature to conformance here - you need biometrics to be added to whatever domestic or Ireland service you actually want to take. Therefore going into airside with an INV boarding pass could lead to endless problems if you end up trying to go to GLA. For everyone's sake it's best not to do this.

Moreover from certain locations (but not all) after you have flown INV-LHR-Somewhere, then you can call to switch the return from Somewhere-LHR-GLA and it will cost little or nothing. It will be free if at some point after ticketing BA changed the timings of LHR-INV. So it maybe worth a call in advance if this is your plan, and that will also deal with any checked luggage. Though an HBO booking will be a lot easier here. I noticed (in another context) that this doesn't always work but you should discuss this with a Contact Centre agent or with a ticketing agent at LHR to see what can be done.

There is no reason to leave off your BAEC number, that just makes life unnecessarily complicated to my mind.