Yes, I believe you can get a boat suitable for cruising the Caribbean for 50K. You of course can't get a large, or new, boat for that price, but for a year or two it shouldn't matter anyway.
The problems will be with regard to repairs and maintenance of the boat. Things break and wear out on any boat with regularity, and with a used boat you never know what is going to break down next, so you should plan to spend a few months with the boat before heading away from the US, just to iron out the glitches.
Costs to cruise. You will find that the major expense is food, and food in the islands (except for the Puerto Rico and the Dominican Republic) will be significantly higher than in mainland US. If you are comfortable with anchoring out most of the time, sailing even when the wind is slight (not much of an issue in the Caribbean where it almost always blows hard and harder), marina fees, and fuel and oil won't be a huge issue. Budget several thousand $$ for repairs/maintenance. You might be able to get away with almost nothing with regard to clothing expenses.
Be sure that you maintain health insurance. Find a professional outfit to forward your mail (family tend to not understand the way things work outside the US, and they don't see mail forwarding as quite as critical as you do. We use St. Brendan's Isle in Green Cove Springs, FL). With the exception of property taxes, I pay almost everything on line.
If you plan to rent out your house you should be sure you have a reliable firm managing the property. The 10% of gross rentals is a small price to pay for managing your home while you're gone.
I've put down quite a few cruising hints/tips/etc., in my Cruising Dictionary: http://www.cruiser.co.za/faq.asp
Check out the links to my various cruising pages.