More a "could" - if there's a mass exodus of coaches and 2nd/U18 team managers it'd be a bit more worrying

I suppose we'll probably get Tait or Baines as caretaker, or a "team" like when we had Dunc for a game or two and he had all the boys helping him.
The job makes sense but not for a manager like Dyche (or Moyes for that matter as he gets thrown back here a lot) - it's more of a future project type where you have to strike a balance between management and recruitment on what to get. In an ideal world, they'd probably have a talk where positions are identified and he should find targets that fit the manager, team and wage structure in those positions and work towards signing them. Not every transfer will be a massive hit obviously, as is always the case anyway, but that's the idea behind it and teams have been doing it for ages. Ideally he should also be the one to identify the manager himself as players are usually cherry picked for a certain style of play.
However, we got Ashley Young as first signing and rumours (which I have no doubt have some truth to them, if they aren't entirely true) that Dyche kept rejecting players as they won't fit how he wants to play. That's why it won't work - an outdated manager with an outdated approach is essentially blocking transfers, whereas a DoF is a team-first position where he's building a squad for this season and next.
Most of our transfers haven't been Dyche type players, but he's not really got a choice so he's playing the younger players (and even at that - rarely where he can help it) out of necessity.
Now, finances mean we're effed sideways so the squad building itself isn't exactly great either, but this should be a platform for mid/slightly lower finish (10-14 or so) this year where we can hopefully add more players next year to go a bit above, it's not an instantaneous thing unless you get some brilliant players for next to nothing.