This is a vague question, IMO. Example: You don't specify the yeast you want to use. - see below*
Let's go back to square one. Probiotics are usually live bacteria and possibly some other types of single celled organisms. They are usually found in fermented foods like yogurt. Baker's yeast in the role of a probiotic is discussed in this review:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3257658/ There are other papers by these same authors.
So your assumption that yeast is a probiotic may have some foundation. Generally the research has been on wild yeasts and Baker's yeast.
This is a guess based on this one review:
If you eat beans, lentils, and other legumes, then the phytate found in beans is hydrolyzed (phytate is an antinutrient == bad, hydrolyze == break down), improving mineral nutrient absorption.
Answer: in this limited context, yes. Yeast in sugar water allowed to bubble (ferment) for a while, and then drunk possibly has some positive effect. You might benefit from yogurt in other ways, so consider other sources.
*Is there some reason you cannot eat other fermented foods? And you do realize there are many kinds of wild yeasts, and other kinds of yeasts humans use other than baker's yeast. If you use Brewer's yeast, for example, you will get some ethanol (alcohol) in your drink, which may have other effects. Wild yeasts could render the drink very sour/bitter and make the drink unpalatable. You may have heard of "sourdough" bread, made by wild yeasts. Sometimes the bread made from brand new homemade starter is really awful tasting, for example.