Does completing the Desmond memories have any effect on the Ezio campaign?
Solution 1:
You can safely ignore them. What they give you doesn't affect the outcome of the game. They're only for storyline and achievements.
Solution 2:
I can confirm.
You can play the full Ezio campaign without even doing one of Desmond's memories.
Source: Desmond's memories crashed every time I stepped into the glowing "load" portal. Thus not allowing me to do any. Completed the game without any issues.