Using QF as the target of query, and assuming you are in transit to airport with no bagdrop and you are down to the wire...are you in a better recovery position OLCI'ed and then missing flight than ringing QF while in transit and telling them you will miss flight prior to OLCI, and prior to checkin (by whatever method) cutoff time?.
There isn't a really silver bullet answer to this.
I'd say that if I were in transit and reckoned I had a better than even money chance of making the flight (i.e. after arriving at airport, sprinting for security, clearing it, sprint to gate before scheduled time of departure hits - around the time they start making personal pages for pax to get going), I'd OLCI to make the deadline and proceed as planned.
If I (then) hit an incident where I know I won't make it, then it's time to probably ring QF and ask them what to do. Elites have the advantage here, of course, as in these time imperative situations it's much better to be able to be connected ASAP. Platinums and Platinum Ones have the distinct advantage. At this point of ringing them, the check-in status is unlikely to have any influence, but if it were much closer to the departure time that I got stuck, it's likely I've already checked in. I think to be moved out, you need to be "unchecked in" before you can be moved as such. I'm not sure / can't remember if telephone agents may or may not have powers to do this, so you may need to "face the music" once at the airport.
With an unchecked in booking, telephone agents might be able to move you successfully without airport intervention.
Note that OLCI (for QF) closes 45 minutes before departure. If you're within 45 minutes and still haven't checked in, again if you think you have a good chance at the airport to touch the totem pole before the 15 minute closure deadline, then go for it.
I think the moral of the story is that there's not a lot that check-in status factors into your actions; if you're going to miss a flight (whether by a hair or by a long mile), you'll just have to roll with the punches of getting rescheduled / credited / just plain cop it.
