Well you can, in a manner of speaking.
What do tier points give you? on BA priority check in and lounge access, rather than frequent upgrades.
Therefore if you:
(a) get an Exec club blue card, you can check in online the day before and drop your bag off (in my experience, you're normally directed to a club desk if the traveller queues are horrible and there is not dedicated bag drop.) You can also access some pretty nice Y/M seat allocations this way.
(b) buy a Priority Pass, which gives lounge access (non BA) at most airports.
I reckon this is a pretty good way of making the travel experience more palatable.