Will a DD368 accompanied with an OCS packet allow me to make the switch from the CG to the Army?

If the CG has a policy to allow you to separate from AD early, then sure. A DD368 is just a piece of paper that's part of a packet to apply for OCS

If you bring a 368 to a recruiter that’s the first step in switching to Army obviously, but I wouldn’t put all of your eggs in the OCS packet. I don’t have the exact number in front of me but since the integration of the new OCS boards going through USAREC, the selection rate is somewhere around 13%. We had a prior service Army Sergeant apply with a masters degree and not a blimish on his civilian or Army record and he was denied. Some big ticket items that seem to help individuals are GPA and what your degree is in. If you got a 3.1 in something like criminal justice, I wouldn’t have strong faith. A high GPA and STEM degree would hold a lot of weight.

Wow... Heavy involvement in Antarctica, Asia, North America, South America, a touch of Europe and Africa, and a pinch of Australia, is not a global enough organization? There must be another reason(s) for you wanting out of the Coast Guard and that's ok... But you can't say that the Coast Guard does not operate world-wide, though.