I don't think it makes a huge difference, and I am not one of those clicking away at T-24, I just do it when it suits.
But the other reason for checking in online is that it is the final check on your ticket and API issues. So if heading to the USA you can work out if you're going to get SSSS (and pack differently, I know, silly isn't it?) or whether the DHS can't find your hotel arrangements in the database. Equally if you have mucked about with your ticket at some point then you may be awaiting revalidation / reissue or an error indicates a Sync issue. More details in the Dashboard thread on OLCI problems. If you didn't have status, not checking in online - and thus potentially not having an earmarked seat - could lead to downgrades and on purely BA metal, an early OLCI increases the chance of upgrades. But those latter factors don't seem to be relevant here, so I think you should still do an early OLCI but I tend not to rush, as it happens. I've got 4 flights in the next 24 hours or less and I've not checked in for any of them yet (I'd rather flooze around on Flyertalk....)