Being immune to chicken pox does not effect ivf success, the reason for wanting immunity prior to ivf is so that if you become pregnant you wont have to worry about getting chicken pox during the pregnancy which could cause birth defects in the developing fetus.
The CDC currently recommends 2 doses for adults that do not have immunity. With that being said about 78% of people will get immunity from a single dose (adding the second dose brings the number to 99%). It looks like your clinic is trying to avoid giving you a second dose by seeing if you fall into the 78%. If you are immune after a single dose then great, no need for a second dose. If you aren’t immune then you can get the booster.
I’m currently dealing with this. I never had chicken pox as a kid. I found out during my first pregnancy that I was not immune so I received the vaccine after giving birth. I was not aware of the recommendations to get 2 doses (and somehow I guess my doctor wasn’t either) so I never got the second dose. During my second pregnancy they again tested me for immunity and I found out that I still wasn’t immune so again I got the vaccine after delivery. This time I’m making sure to follow up and I go in today for my blood test to find out if I’m finally immune. If I’m not immune then I’ll get another booster and check again.
The chicken pox vaccine is a live virus and that is why you need to wait 30 days before getting pregnant or doing ivf. There is absolutely no reason to have to wait 1 year, I would challenge them on that if that is indeed what they want you to do.
Best of luck to you!