"Yet Paul makes it clear he was not sent to baptize even though he did."
Here's what Tertullian says on this:
"But they roll back an objection from that apostle himself, in that he said, 'For Christ sent me not to baptize;' as if by this argument baptism were done away! For if so, why did he baptize Gaius, and Crispus, and the house of Stephanas? However, even if Christ had not sent him to baptize, yet He had given other apostles the precept to baptize. But these words were written to the Corinthians in regard of the circumstances of that particular time; seeing that schisms and dissensions were agitated among them, while one attributes everything to Paul, another to Apollos. For which reason the 'peacemaking' apostle, for fear he should seem to claim all gifts for himself, says that he had been sent 'not to baptize, but to preach.' For preaching is the prior thing, baptizing the posterior. Therefore the preaching came first: but I think baptizing withal was lawful to him to whom preaching was."
"So, can an unsaved man have the Holy Spirit of God ?"
This is a trick question, right? It all depends on what your definition of "saved" is. If its the innovative Protestant idea, I wouldn't know, but I tend to doubt it. If its the Eastern or Western theology of The Church you are talking about, the answer is clearly and absolutely yes.
I think this is the most dancing I've seen around scripture, saying one doesn't need baptism. I expect it when talking about Our Lady, but baptism?? whew.