Weird that it would have to be post-DSC. Pike is a famous hero before his DSC appearance already, after all. And the hair and makeup on Mount is ageless enough; he could go ten fictional years either way without a need to alter his looks.
Fewer writing constraints in the years long before TOS than in the ones immediately before it, too. As for my personal agenda, if they're going to make heavy use of the bridge set and the CGI model, nicer for those to be from the unseen 2240s-2250s than from the 2260s, for visual continuity reasons.
In any case, the less we get Mount's Pike the better IMHO. A titular show could ruin it easily enough. But Paramount is likely to think the other way.
Timo Saloniemi