I would say that while I loved everything I did while I was in school, it was the outside the classroom opportunities (student government/organizations) which were generally restricted to just undergrads that really taught me the most useful skills and connected me to a much broader network of people that I've found very helpful in my professional life. While I wouldn't say that it's a bad idea to "sneak in" I don't think it's the same experience/value as the regular undergrad program.
What isn't often mentioned is that the courses at HES are often live streamed from actual Harvard College courses. Same course, same grading. I've directly questioned my profs about this and they say that they don't differentiate between students in either population even if Harvard sometimes lets people believe they do.
The CS courses are the bomb, BTW. The CS faculty at Harvard are very supportive of nontraditional students.