The title and opening post are a tad bit different. I would suggest rewording it to something like "What if Belarus joined Russia through a Referendum?" or something. And I have to say, it seems fairly impossible. When Austria made a referendum about Anchluss (kinda sorta) it was more for showing whether or not Austrians wanted to stay independent, and it led to murder and invasions. Or threats of it. The Germans weren't really all for that 'voting' stuff. Set a bad precedent. Anyways, the President of Belarus is already grooming his young son to take over his job in the future. And, while I am sure the Russians would be happy if Belarus joined them, they are content having numerous former-Soviet countries that economically and diplomatically keep in line with them and add a half-dozen votes in international organizations. Plus it is always good if you can point to a country and say 'look, THEY are the Neo-Stalinists looking at the glory of the USSR'. Besides, the Russians got small satellites that broke off from Ukraine, Georgia, and Moldavia in part because they either were ethnically Russian or the states they were in didn't give enough minority rights. Apparently. For Belarus you have a large country bordering multiple states, and most of your own coethnics are in the same country as you.
If they DID join though? Well, I guess there will be a period of franticness from the EU. Gonna be problems with the Ukranians claiming the votes are rigged and that they need to be careful or they will be next (then throw insome talking points about the Holodorm, Potemik villages, etc) while the Poles and Balts either make sure that NATO has their back or take measures into their own hands. Not be invading, but upping their militaries even further.