There certainly are those Jesus mythicists who would also deny that there was a historical Paul. But for many mythicists, perhaps the majority, the historicity of Paul and the authenticity of Paul’s letters is in fact important to their argument, since their case for mythicism focuses much attention on what Paul allegedly did not say about Jesus.
There is an irony here. Some mythicists actually do use the same tricks to deny the historicity of Paul as are used to deny the historicity of Jesus. Yet on the other hand, many of the arguments used to deny the historicity of Jesus by mythicists who accept that there was a historical Paul could be used to argue against Paul having been a historical figure as well, if the degree of skepticism applied to Jesus were to be applied consistently across the board.
For instance, many mythicists claim that since there are (allegedly) no early non-Christian historians that mention Jesus, he probably did not exist. Yet none of these figures they typically point out (or in the case of Josephus, claim) failed to mention Jesus – from Philo and Josephus to Seneca the Younger – mentions Paul, even though Paul is supposed to have traveled more widely than Jesus, and to have spread the religion we today refer to as Christianity, even going to the very capitol, Rome itself.
In none of its forms does mythicism deal with evidence in the manner that historians do. But the fact that few mythicists deny that there was a historical Paul shows that even in their treatment of figures connected with Christianity, there is significant inconsistency in how most mythicists deal with evidence or apply their arguments.