I believe this has come up before, they are not entitlement to be put out when they are required the next base on a walk so the run should count. so they are protected in that sense.
Each runner advances without liability to be put out if forced on a walk, but that does not mean the run automatically scores. The ball is live on a base on balls and all base runner rules still apply. With 2 outs if one of those runners goes past the base they were entitled to and gets put out before the lead runner touches home plate the run does not count. NFHS used to count the run regardless, but has changed their ruling and it the case play was provided above. USA has never said the run would count.