This is a hard call.
I suppose the best person to advice if beta-thal will be passed down to the next generation is to understand this condition from your own doctor. With a better knowledge, you then go up to your wife and convince her to do a thorough blood examination.
Honestly, if this trait does not already runs in both yours or your wife families, the chance could be like 25%. If your spouse insists of not taking a blood test, you decide if you still want to start your family planning. We can't really advise you since we aren't expert.
Btw, there are many successful pregnancy of women with multiple cysts and fibroids. I am one who has multiple fibroids (as large as 11cm) and an anaemic (that runs in my family) now is a mother of a 12 month-old healthy girl.
Best of luck to you in convincing your wife to get her blood tested.