Yes, If you have a cac card, you need approval and will likely need to check in/out with embassy, most likely by telephone.
And it's not because of any clearance, you probably don't know anything of value, it's so they know you are around, should the local police pick you up on a drunk and disorderly charge.
Still probably be a good idea to call the HPSP office and ask...if they make us let them know our location when there is a hurricane off the coast they probably like to know at the least that you will be out of the country
There's probably some rule, and I do remember being told that we were not allowed to go to Mexico. I went out of the country several times during medical school and even mentioned it on my residency CV and never got answer questions about it.