McLellan probably would've been coach anyways; it seemed like there was an agreement between MacTavish and him before they won the lottery, and as others have stated, it's rumoured he wanted to stay in the west (I believe he has family in Saskatchewan as well?).
Todd McLellan was the contracted coach of the San Jose Sharks before the draft lottery. There was no "agreement", but there was a match that made all of the sense.
Chiarelli? Nope. MacTavish was caught by surprise by his firing; I seriously doubt this happens if the restructuring was solely due to Nicholson's forensic audit, although his 'another development year' comments might have been what did him in, not the lottery win.
Nicholson claimed he moved on Chiarelli because he was a cant-miss GM.
To me, the question isn't "would MacTavish have been fired" as much as "would Chiarelli have come". Chiarelli only had a few potential landing spots and they're all rebuild cities (Toronto and New Jersey in early stages). He had a pre-existing relationship with Nicholson AND wanted a level of autonomy he wasn't going to get in Toronto.
Kevin Lowe, IMO, was being transitioned into his new role whether the team won the lottery or not, and I'm of the opinion it was also partly his choice. I think Nicholson was brought in last year to be groomed as his successor, and that's the way it ended up.
Nicholson was named CEO before he even set up an interview with Chiarelli, meaning he was never groomed to be Kevin Lowe's successor as President of Hockey Ops.
Kevin Lowe did try to leave the POHO position the year before and he was given the Vice Chair position in OEG a year prior, so I don't doubt it was always the plan for him to leave
My money is on the same stuff happening.