Actually, there is no such thing as an "H Transfer". If you move from one institution to another, the new institution has to create a new H visa for you. The fees and hassles are all the same -- with only one (big) exception. If your original H visa was under the 65K visa cap, then any transfer remains under the same cap. So, for employees with H visas that are under the cap, a transfer simply allows them to move to another employer without standing in line again to get a visa. Since most academic medicine programs will be exempt from the cap, it doesn't matter at all.
So, whether or not your neuro program will sponsor an H for you doesn't matter for the prelim -- they will need to do a complete H visa application for you in any case (unless your prelim is at the same institution as the neuro program, then you only need one H visa since usually you'd be hired by the GME office, not the individual programs.