I don't believe he'll struggle at all. If anything he'll be better than he was and here's why. Unlike Rose or Rubio, Rondo has something to prove with the new team. With KG and Paul gone, solidifying the claim he's been making for the past two years that he is the leader and that this is his team, will be his main goal. To prove that he can be rebuilt around. Here's a new coach (who he's had a close relationship with), and a new rebuilding team. He's going to want to prove that he can truly carry this team.
And I wouldn't in a million years compare Rose's heart or competitiveness to Rondo's. Derrick Rose is a wimp of the highest class order. Rondo is warrior and we'll see it soon enough.
The advantage is has over Rose or Rubio is that even if he struggle as far as scoring, it wouldn't be a big deal because he was never great in that department anyways. So, not much expectation there.