Answer

I don’t know. It is clearly forbidden, but if it were established after the fact that the murdered person had indeed committed murder, then perhaps the blood avenger would be exempt.
There may be room to connect this to Rabbi Akiva Eger’s note on Tosafot, Makkot 5a, according to which there is no liability for execution before the verdict has been issued by the court (that is, the religious court’s ruling creates the punishment and does not merely reveal it). According to this, it would seem that as long as the religious court has not ruled on his case, he is not liable for death. Still, one could distinguish between that case and this one, because here we are dealing with permission for the blood avenger, not with the murderer's own liability for execution.
I should note that in practice it cannot be established after the fact that he was liable for death, because if he is dead, the religious court will no longer try whether he had murdered in the past or not. Perhaps this could happen if the blood avenger killed him during the trial, before the final verdict. But even that would not be completed, because a person is not judged in his absence.