I've never played DW in a PbP format, but I think that it could work very well with a little modification: the GM makes all the rolls. In this way the player is free to write about their characters and the GM doesn't have to wait for the roll. Otherwise the action could slow down a lot when dice rolls are needed.

Example:
-Player: I do A and B
-GM: ok, so (rolls +X and +Y) it happens this and that. What do you do?
-Player: well, now I do blah blah blah
Is better than:
-Player: I do this and that
-GM: ok, roll +X
-Player: I got 9
-GM: Well it happens this, now roll +Y
-Player: I got 11
-GM: good, it happens that. What do you do?
-Player: well, now I do blah blah blah