We will have to wait for the official stance by the CDC on this. This is just my opinion below based on what I know. It doesn't or shouldn't reflect on what any given individual should rely on.
The precise answer is we don't know for sure. In order to find out for sure is to see clinically what happens when it does happen. That's what is going on with COVID immunity and the new variants. We watch what is happening in the clinics and hospitals to determine if the current vaccine is protective or if it is time to get a booster.
If you look at the stated official protective effects of the smallpox vaccine it says it is good for 3-5 years and if you are in a special needs group or high-risk group like if you work in labs working with smallpox then you need boosters.
We often have to use test tube markers in order to predict how long immunity lasts by measuring neutralizing antibodies in the blood. These are termed longevity studies and in the case, of vaccinia which is used as the smallpox vaccine, we have found that greater than 97% of the people who received the vaccine had neutralizing antibody titers greater than 1:32 decades later. We are assuming that when one has a titer less than 1:32 they are not immune and those greater than that as being protected against smallpox.
The link is one longevity study done in 2009 and they state that those under the age of 35 would not have gotten the vaccine which at present time would now mean those under 45 years of age would not be expected to have taken the vaccine which ended in the 1970's I believe.
The vaccinia vaccine is only about 85% effective against Monkeypox under ideal conditions.
It would be assumed on a population scale that most people previously vaccinated against smallpox would be immune to monkeypox. It would obviously vary on a case-by-case basis. If there would be a mass vaccination campaign then those under 45 years of age or so would be prime candidates first when supplies are limited before boosters would be given to those previously vaccinated.
Immunity from Smallpox Vaccine Persists for Decades
A Longitudinal Study
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2610468/