Yes and no. I do think that Edna seems to be presented as another character just like Earl, who believes that he can begin again through moving to a different location and that running away from your troubles can be a good way of living your life. Note how Edna responds to Earl when he, completely out of the blue, suggests that they go to Florida:
Why not? My datebook's not that full.
The fact that Edna seems to agree with Earl's decision and that she is another character who doesn't really seem rooted to any location or locale means that both of them seem conviced by the vague hope that running away from their problems will actually make things better. Edna is therefore partly to blame because of the way that she does not challenge Earl to face more of the reality of life and to confront his problems.
However, at the same time, the overwhelming message of this short story seems to be that we have no control whatsoever over the cards we get dealt in this game of life. This of course has nothing to do with Edna. She, just like Earl, is trying to do the best she can with the cards that she has. This does mean that she leaves him, but all of the problems that Earl faces are not her fault.