People did recover from MEV-1 (the fictional virus) as they mentioned at one point in the movie the mortality rate was between 25-30%. Based on the numbers that were thrown around over the course of movie, the estimates are the fictional virus killed 25 million people. The thing with the movie virus, though, is a person infected with MEV-1 typically became symptomatic within 24-48 hours and succumbed to the virus within 4 days. A nationwide lockdown of a couple weeks would pretty quickly halt a virus that was that fast acting, unless it lived on surfaces for a long time.
With regards to those whose birthdays were towards the end of the vaccine distribution period - by the time 60% of the population had the vaccine, herd immunity would start to take effect decreasing their chances of catching the virus anyway (and all those who are now immune could starting doing errands, etc. for those still not vaccinated).