Well I don't know to what extent Annie resembles her Muppeteer. However, there is at least one scene on TMS where she almost certainly did. ...
In the Leo Sayer episode, there is a scene in which she saves Fozzie's act. Afterwards she and Fozzie are comming off-stage and there is the following interaction between Annie and Kermit
Kermit: "Well done Annie Sue"
Annie: "But I didn't do very much"
Kermit: "You just saved Fozzie's act!"
From what little I've read/heard/scene I get the distinct impression that modest self efacement's rather similar to her performer.