A P323 opposite me for a while had spent a few months in the Caribbean; Florida - Caribbean - Florida before being trucked to CA. It should be no problem for a well-found 323. And a recent crewmate sailed a 323 from California to Nicaragua. Took a few months, and some of those crossings are nasty. Very nasty.
I think what you are talking about is more what I think of as "offshore coastal cruising" as opposed to "blue water cruising".
Spend some time looking at the work Richard did on his boat:
http://rollinscs.com/boatpages/projectspage.htm. IMHO, it is the gold standard for getting a 323 ready for offshore cruising. I would have thought if you followed his example, you would have a boat more than capable of what you are considering.
If you watch the weather, 100 mile crossings should be a snip. I don't know how much you have been out in heavier weather, but as an example, I was out a week ago, the winds were gusting well over 30kn; with a double reefed main and motorsailing (I was solo and lazy) it was singularly unexciting - the 323 is a weatherly beast, and loves a good blow. And where I sail (SF Bay Area) we are often sailing in 25 knots.
As for blue water cruising, I would hesitate a bit doing transatlantic or transpacific. Is the old girl strong enough? Sure. She is well built, even overbuilt for her size. But the 323 was not designed as a bluewater cruiser; for example, the high freeboard and wide beam could make her uncomfortable in a sustained gale, and the shallow keel is not optimal. Provisioning her for a couple of months would also be tight. Could you do it? Probably. For any serious offshore work, securing everything as Richard did is just the first step. Personally I would also consider replacing the (plastic) portholes with something more robust; of course, replace standing rigging and definitely chainplates, and probably beef up a wide range of equipment and attachments. Secure the splashboards, add/improve the seals on the lazarettes, add additional cockpit drainage, etc etc.
If I wasn't on the wrong side, the Caribbean would be beckoning me too! Good post; I'll be interested in what others say.