doubtful there will be any serious investigation or consequences if this in fact occurred. he will just be moved to a less glamourous post at worst. but the party will take care of him.
There would be investigation but mostly at party level. This is not going to be a criminal investigation, I don't think even the lady is asking for a criminal investigation. It is more 'why didn't he divorce' than 'why did he do it to me'. Sometimes, investigation on something minor can lead to major issues, if corruption or other things are dig out. All these will happen in background, people won't have the joy of the drama until it is over.
Zhang Gaoli is retired but censorship rules means that all news of this is pretty much censored in China
He is 75 and has already given up most of his duties.