Haeckel and the whole over reliance on dubious embryonic analysis played a huge role in Darwin's argument and later evos in initially gaining acceptance for evolution.
No, Haeckel's drawings had nothing whatsoever to do with the development of Darwin's theory nor the arguments for that theory that he presented in "On the Origin of Species by Means of Natural Selection". Mainly because Darwin's book was published almost a
decade before Haeckel drew any of his infamous embryological diagrams.
Unless you think that Darwin invented time travel in addition to evolutionary theory.
It became sort of a mythic concept, recapitulation and the Biogenetic law, so much that it's been very hard to stamp out despite the claims often being wrong, and not really logically supporting evo theory any more, nor being that critical to it.
Haeckel's drawings were used in most textbooks to introduce people to evolutionism until around 1998.
What's sad is the evolutionist community cannot seem to divorce themselves from Haeckel and finally accept recapitulation just isn't so.
You have no idea what the modern recapitulation theory is, nor how it differs from what Haeckel's ideas were. Because if you did, you wouldn't say nonsense like the above.
Especially since Richardson's 2002 paper lays out exactly what Haeckel got wrong, what he got right, how his ideas differ from modern ideas (honed with more than a century's worth of additional knowledge gained since Haeckel's drawings first appeared), and even how his ideas are compared and contrasted with those of von Baer (EDIT: and those of one of Haeckel's harshest contemporary critics, Wilhelm His).