I'd be staggered if it didn't happen. But then, I was pulling my hair our last summer, never mind January.
Last summer I think Thelwell (and most naive blues, to be fair. Most rated the summer window highly) figured defence and midfield was a priority. They were wrong. There's no illusion anymore.
It's DCL/his partners who are sharing the videos. Pretty common for players to be "look im working even when off" on their social.
Last summer many thought it'd be ok up front because DCL was training again and Lampard was happy even though Richarlison hadn;t been replaced. Then DCL picked up that injury and the whole club - manager, team and fans - realised the implications when the club failed to sign a replacement in the final week of the window.
IMO Dyche will keep faith with DCL too. He'll add another forward, but even that'll be a gamble.
There's no one willing to make the big decision at Everton to get shut of Calvert-Lewin or to marginalise him to the point of buying two forwards so where if he does get fit then that's a bonus because we'll have 3 to call on.
The Calvert-Lewin situation is a microcosm of all that's bad about Everton right now: a club that cant make tough decisions.