I have three licenses myself, they are independent from eachother but you have to deal with currency issues with each one, depending on the training program that your airline has (Boeing approved program, the training is approved by the FAA to conduct training outside of the US....etc.) they might accept it to meet recency requirements in the US, but some training programs abroad might not be, a couple of my friends that fly in China have to rent a GA contraption a couple of times a year for that purpose....!