Can anaphylaxis cause congestive heart failure?

Anaphylaxis: Complicated question, yes it could in the right situation. Anaphylaxis of its own can have a form of pulmonary edema associated so the question is complicated.

Only at the moment: It may cause cardiovascular collapse when the anaphylaxis is severe. This is more from reduction of plasma volume in the vascular bed than actual cardiac failure- but the result would be the same since the heart will not be able to provide enough blood supply to the body. CHF is from the heart's inability to pump enough blood through your vascular system despite adequate or even high plasma volume.