I think they do, but at a steady pace, not all their users on that exchange in one fell swoop.
Re your two examples, as far as I'm aware no WBC service is available on O2 Access, and I can't remember seeing it mentioned on Sky Connect either. Both are "up to 8Mbps" services, supplied (these days) through IPSC I expect on non-WBC, (though perhaps there are still a few BT Centrals around), and a mix of that and transferred ones on WBC exchanges being placed on "ADSL Max" type profiles. (Not to be confused with IP Profiles).
A case in point is Plusnet. They automatically transfer customers at some time after the upgrade, but I think keep them on an ADSL profile not ADSL2+ for a while. However if a customer is aware that their exchange has been upgraded they can request an immediate move to ADSL2+.
In the end, each ISP will have its own policy so I don't think a general answer can be given. If you want to know for a specific ISP then I may be able to dig something out. If you are thinking about Orange via BT Wholesale White Label then I have no idea.
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