Would the 245i allow him to stay in the country or would he have to leave when we begin the adjustment of status?

You should be able to file an adjustment of status by using the old 245i filing. If done right, the entire process should only take 3 to 4 months. And he doesn't have to return to Mexico.

Assuming the previous marriage was not fraudulent and he has no other basis of inadmissibility, he may remain in the US and adjust status under 245(i) once he marries you.

If he is indeed protected by 245i filing, he would not need to leave the U.S. to legalize his status.

It is possible for your husband to remain in the United States and apply for adjustment of status through 245(i); however, it will depend on the circumstances of his prior marriage and his immigration history. If his ex-wife's I-130 petition was not fully adjudicated, to remain eligible for 245(i), he must submit sufficient evidence to establish that the prior petition was approvable when it was filed with USCIS. The evidence can include, but is not limited to, proof of cohabitation, joint bank statements, joint health insurance, joint lease agreements, joint tax returns, photos, affidavits, birth certificates of any children born from the relationship, etc.

245i allows an individual to adjust status in the US. Work with an attorney to make sure he is actually 245i eligible.