Mattpilot,
Foreign pilots can still get typed in the US provided they pass the FBI`s screening process.Last I heard (and this is a few months back) the screening process took about 45 days.If I`m not mistaken (again this is slightly dated info) the applicant has to provide the training facility various information about him-/herself and the facility sends this info through to the Department of Justice and the FBI - then you get to wait.Things might be moving along at a quicker pace nowadays though.Also heard something about that the training has to be under an approved part 142 curriculm, meaning you can`t just put some cash on their front desk to buy a couple of hours in the sim... and we all know why
With regards to already typed pilots there is really no problem at all.This is a good thing with regards to recurrent training and such so they can keep the costs down (compared to Europe).
I still haven`t found any info about groundschool alone (typerating courses), so I guess there aren`t any restrictions on those since you`re just learning systems - not actually maneuvering the aircraft.
If you`re thinking about obtaining a license outside of the US I think foghorn is on the right track.Allthough the JAA license is accepted "everywhere" it is also a major hassle to get.The Oz licenses are a lot quicker to get - and cheaper.The same with regards to the Canadian ones.Just keep in mind that the FAA certificates aren`t accepted everywhere (though validations are possible) since they are not "Straight" ICAO licenses (too many differences)...and most of the other countries accept each others ICAO licenses (sometimes the only requirement for a conversion between 2 ICAO licenses is an written exam in Rules & Regulations).
Hope this helps you out!