The warts will not show up again. I am not sure if the virus will still be present in the body or not. I know once as you have mono, it stays in the body, so I think it is similar to that.
But if you want post in HPV community, they will have better info for you.
if the body clears the genital warts.... will the virius still be in the body? or will the warts never show up again?
That is correct. And it will typically clear in 6 months to 2 years.