Disclaimer: I'm not a Blue Angels pilot so don't know their exact procedures/limitations, but have done a fair share of military formation flying.
It is possible, it's just a more "bumpy" ride. Not a huge issue if the turbulence is not severe enough (or of a "rotor" type) to cause uncontrollable rolls in three dimensions.
When flying formation you are separated from other aircraft in three dimensions. In turbulent weather conditions the aircraft position usually results in vertical displacement, not so much in horizontal displacement.
This means the aircraft will not roll into the adjacent aircraft (the roll effect happens when you fly into wake turbulence or through rotors for example), but do more of an "up and down" jump.
The same air disturbance will effect several (if not all) aircraft in the formation, sometimes with just a tiny delay.
Also, the heavier and faster the aircraft is, the less effect the same amount of turbulence will have. If weather doesn't permit a small single-engine piston to fly formation, it may still be workable for jets.
Ultimately, it is up to the flight lead to:
- determine if conditions permit close formation
- fly the formation to avoid known hazards (for example if the wind is from the N, don't fly on the S side of hills/mountains)