I don’t understand oomis’ comment. First it says it’s Muttar, then goes on to say that Bidi’eved the child is not a Mamzer.
By the way, the child is considered Paggum, whatever that means to you.
When Rabbanim are Mattir couples to use this method they are always very careful that there should be strict supervision making sure nothing gets mixed up. Although the Gemara is Mashma that someone doing this can marry a Cohen Gadol, I cannot imagine the child not being a Paggum.