Hi, Justakid, and welcome to the forum.
I love these kinds of crazy ideas -- most of us around suffer from them, so you're in good company.
I'll give you my two cents, keeping in mind that it may only be worth what you've paid for it:
Working around the world: Will vary a great deal from country to country. Some places you definitely don't want to get caught breaking their labor laws, you'll be in for a long stay, but not in their best hotels. Others don't seem to care. Bartering in the cruiser community is very common, but you need a skill with which to barter (diesel
mechanic, heating/air conditioning/refrigeration,
computers, electrician, etc.).
Going around without turning on an engine: Not likely. Sure the old square riggers did it, but you'll quickly find many instances of not enough
wind, or
wind coming from where you want to go. Not to mention simple manuevering and
docking. Although they are called "auxiliaries", they are pretty much essential.
I suggest you start with a good book or two. Hal Roth's book on sailing around the world is quite good. There are others, too. Don't take any of them as necessarily "gospel", but rather as that person's
advice and experience.
Cornell's World Cruising Routes is an excellent resource for planning.
Hope this gets you going.
ID