Probably yes. In the literature Small pox vaccination protects against monkey pox. And such DNA viruses are very stable.

The interesting part is that you can get pretty much any vaccine except the small pox vaccine now. Figure that out. They’ll give a six month baby a hepatitis b vaccine in case it has… sex or shoots iv drugs? But vaccinating for the most deadly disease ever? Can’t do it. The rational is that there’s no need given small pox has been eradicated. Yet many of the pandemic scenarios specifically cite small/monkey pox as the disease vector precisely because it’s bad and no one is immune any more.

The responsible thing would be to allow the vaccine to be taken voluntarily by adults. A certain section of the population would become immune and bring us much closer to herd immunity and either protect against an out break or very much slow it down.