BA does occasionally upgrade elites (its own and other OW) to "sample" the next class of service if there are open seats. There's no consistency to this, however, and it does not happen just if WT is overbooked. I've had this offered three times when flying YYZ-LHR-YYZ in both directions, from WT to WT+. I'm paged in the lounge so it happens after checking in at the airport.
I don't expect this to happen often (and have never had it on LHR-JNB/CPT, another route I frequent on my own dime, though a friend has) but it is nice when it does. The main benefit of WT+ is they serve The Glenlivet instead of BA's standard economy offering. See what happens next month when I'm on BA again.