I was just wondering if it were possible to go e.g. from track 1 to track 2 without needing to go through any gates that require a Diabolo Pass. I'm not planning on visiting the airport, just the train station.
It should be possible. The Diabolo surcharge is checked at a row of automated gates between the foyer of the train station and the rest of the airport. You can go up and down the stairs leading to the platforms and around the foyer before going through the gates. Facilities are minimal (maybe a toilet and of course some machines to buy a Diabolo pass if your ticket doesn't include it) and staff is there to guide the people leaving to the airport through this peculiar process.
That's how I remember it and it is confirmed by the Belgian Railways website:
It is still possible to take a connecting service at Brussels Airport-Zaventem station, without having to pass through the gates.