It's a shuttle pickup, so I think the only worry would be getting to the start if it was on the Friday.
I was thinking about it more enjoyment / fitness wise. If it would be better to do the Blue Tier/ Atlas first up while fresh instead of after a day of shuttles...
To give you an idea of the time:
It takes about 1 hour for the shuttle from Derby to the drop off at the top of the Blue Tier.
Bay of Fires 13km takes about 1 hour of riding (a bit less if you faff less).
Then another 30+ minutes to get back to the top again.
Blue Tier takes about 2hrs, you could do it faster but you want to enjoy it and have a few stops and maybe even the odd mechanical.
So that's about 4 1/2 hrs from leaving Derby until you get to lunch, working backwards you would want to get your orders in at the Weldborough pub by 1:30pm, that means you want to be leaving Derby no later than 9am. It is doable to get off the boat and be in Derby in 2hrs 30min, so it is all possible but doesn't leave much room for delays.
Atlas is then another 20min of shuttle time and another 1hr and a bit of ride time.
Last time I rode it we started at 8:30am from Derby and it was about 4hrs of riding time and 52km. I can tell you now the beer tasted fucking good at the end of that day!