builditbill, there is no problem air drying the wood before putting it into the kiln. The biggest issue is that you'd be handling the wood twice. I recommend end coating the logs (Anchorseal is my first choice) before milling them to reduce the end splitting. The catch is in knowing the moisture content of the wood going into the kiln so that you can bring it in at the right point in the drying schedule.
Exotic woods can be tricky, especially if the species is unknown, since the properties vary so much. In this case, you would absolutely need to know the moisture content. Get a pin-type moisture meter. For the exotics, you may want to perform an oven-dry weight test to calibrate the meter to each species. That will give you an idea of whether you want to kiln dry the wood, and where to start. You can't just throw a mixture of species and moisture contents together in a kiln and get good results.
Check out these links from the Forest Products Laboratory. They will give you a good foundation on drying wood. And let us know how it goes!
Air Drying Lumber
http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr117.pdf Drying Hardwoods
http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr118.pdf