The smartest thing to do would almost certainly be to simply ASK some one in authority at the CU how much they know about their institutions policies on credit cards. Anytime you are talking about an organization with 3Mil members and 173 branches it is pretty unrealistic to not encounter a lot of specialization.
www.nfcu.org
What you need is a "generalist" who is capable of answering your SPECIFIC situation in an honest way. My hunch is that you are better off not doing anything until you have your new savings and checking accounts all setup with NFCU so that they have all the data in the system about your current status with the organization. Once you do that it may very will be that they sorta automatically set you up with a "generic" Visa account. If you want a credit limit increase they'll have a customer service phone line for that and if your request gets rejected they probably can kick you up to a specialist. The other way to handle this would be ask the question ahead of time, but honestly the odds of the decision NOT being baked into some computerized system is pretty small. I would not be at all surprised if even the NFCU relies on a third party to handle details of their credit card operation instead of handling this all in house.
The use of third parties for revolving credit cards is very common, in practice the behaviors of consumers with revolving credit is VERY VERY different than the skills and systems needed to manage the fixed term LOANS that almost certainly originate and administer completely in house. You will only confuse folks from one side with questions they really cannot be expected to answer...