Had a friend who went to the MPA-ESP program straight out of undergrad (orientation was about a week after graduation). While the experience might vary, I think it is to your advantage for the most part. If you've taken science courses in undergrad, the first semester will be relatively easy since you'll already have the hang of sitting through lectures and writing lab reports etc. But if you think you might be too worn out by the end of graduation, best to reconsider.
But, from what I've heard, It's a lot more doable than one might imagine.