Hmm, could be. The whole "interphase" thing apparently connects different universes/timelines in inexplicable ways, after all; we can't necessarily assume the connections are always between the same universes.Unless that Connie crossed over from TOS Prime, prior to Temporal Cold War impacts upon design...
Of course, apropos the OP's question in this thread, that would imply that DSC (and ENT before it) aren't necessarily in Trek's "prime" timeline as we think of it (i.e., as comprising the shows we remember watching). Or, conversely, that the "prime" timeline actually only includes events depicted in ENT and thereafter. (It's not unreasonable; the "Pegasus" interquel in "TATV" and the flashback scenes in ST09 can be read to have similar implications.) Either way, though, that would mean that for all intents and purposes all bets are off and the future is unwritten, so "prime" or not it would amount to a reboot in all but name.