Based on the situation desctibed by the questioner, it would typically be the responsbility of the DoD Component organization who hired to FSN (via the US EMB) to fund the training requirements that the DoD Component established for the FSN position.  Unless the DoD Financial Management Regulations (FMR) or DoD Component imiplementing policies specifically prohibit the use of a training GPC (rather than some other method of payment), then there should be no issue using the GPC to pay for the FSN's training costs under a valid SF-182. 

However, we recommend that the questionner consult their local Comptroller or Budget organization to confirm that the DoD FMR and DoD Component implemeting financial policies contain no restrictions on GPC use in this situation.