Does H4 visa need a separate I797?

Your husband's H4 only depends on your h1b. Just legally residing in the United States.

Your husband won't be able to do any work in America, and he won't have any income.

So you just need to prove your marriage to the immigration and visa officers. Of course, if you get married temporarily on an H 1B visa, the Immigration Bureau determines that your marriage foundation is unstable or your motives are not pure, and there is no reason to refuse to issue an H4 visa to your spouse. At least during the visa interview, the visa officer can't refuse the H4 visa and can't give the immigrant tendency, because the H 1B/H4 non-immigrant visa itself can make the visa holder have the immigrant tendency.

You need to talk to a lawyer.