Someone can probably give an official answer, but I can offer that I have 750 people in my family tree right now and have not noticed any change in performance. I'm sure there are plenty of people with larger family trees than that. Note that there is some upper limit. From the FAQ:
Q: Why can't I add more distant relatives?
There is a limit on which relatives can be included in a tree, based on their distance from the tree's founder. This limit helps ensure privacy for family members, and prevents the tree from growing indefinitely. If you reach the limit, click the 'Create new family' button to start a new family branch from the selected person.