I agree that the change is unlikely to have significant effect on IHA's influence over the Imperial Family. However, there is a chance this new Government will go ahead with changes in Constitution (abandoned after Prince Hisahito's birth).
It will be interesting to see what course the new Government takes on the succession issue.
I agree with everyone here - I think the new government will have a huge number of other more political/administrative issues to attend to before considering any changes concerning the Imperial Family or the IHA.
However, I understand that the IHA is a governmental body/department looking after the Imperial Family and is run by a very conservative, "old school" way of thinking, and so it is not inconceivable that changes in the way the IHA is run or perform their job may occur at some point in the future