I am an experienced hire worried about my age. Would taking an eMBA make a measurable difference in my application?

It depends on the age and number of years of work experience.

If you have under 10 years of work experience, then it can help if you are going to a target MBA school.

If it is a non-target eMBA program, then it likely won’t make a difference. There isn’t an age cutoff but the older the person gets, the harder it is to break into consulting.