Not sure their fans would be overly happy with a polite and slightly 'posh' sounding southern Englishman? They tend to wear their whole 'angry Celt' vibe pretty proudly, we all see the nonsense that goes on from their fans. I think they'd struggle to warm to Eddie. The likes of Martin O'Neil and Neil Lennon throwing bottles around and making their presence felt on the touchline seems more their cuppa tea. Eddie studiously and quietly standing there soaking up a game and mulling it over would get their heckles up the first moment things didn't go well.
Not sure what Howe would think he'd achieve there. Winning various Scottish pots obviously, and winning silverware is something that's unlikely here (Championship aside). So how much does winning Scottish silverware actually mean? It might be something he'd like on the CV, don't really know. How does it weigh compared to his well publicised personal aims for AFCB? Only Eddie can answer that.
One thing we can judge with more evidence is how player recruitment compares. We know Howe loves his technical coaching day to day, that's what he lives for. Being able to recruit talented young lads who he can develop is what he wants from a job. So does a bigger club with less money but an exotically wide recruitment net trying to find value, or a smaller club with more money but mostly focused on British and (more recently Spanish) recruitment, lend itself better to that? Comparing recent signings suggests we might have an edge there. As when at their previous clubs, the likes of: Cook, Brooks, Solanke, Ake, Lerma wouldn't have been going to Celtic, for the money it required to get them. And we already seem to be developing another Howe recruitment plan for the summer if links to Mason Mount are to be believed.
I guess the commute from his roots here might not actually be such a big deal, flying up and down might well be better than driving to northern England. And whilst I don't know much about Celtic's training facilities, it's a fair bet they're much better than ours.