Interesting analogy SG, but not entirely correct. Scientists develop new technology, but then rely on the military to find ways to utilize it to maximum effect. As a scientist myself I can vouch that many of the products developed aren't used the way they were originally intended.
With that in mind if you really want to mimic reality then you need to have a system whereby new cards developed by the support personnel can be directly implemented into the war. Giving a team a card advantage through existing mechanics serves only to create an imbalance in the actual fighting that is thematically not directly related to anything done by the support team. Something as simple as having the support team design a new card each week that their team would be allowed to add to their vault as a "free" swap of up to 4/6/whatever total cards would make perfect sense. This preserves the balance of the fighting but also allows for the "new" technology developed by the scientists to be implemented. More importantly, it forces the designers to have a purpose for their cards that will be useful to their war teams current vault and strategies. I can see this making the PvPers/Fighters and Designers/Scientists coming together to work towards a common purpose, which really is what creates the success in a war. Having your support guys develop a new land mine when you are fighting naval battles really doesn't give any advantage, no matter how amazing and advanced that mine might be. Somehow the cards developed need to have some direct tie to the cards and strategy of the war team, and that would best be shown through implementing the cards directly into the war. Any other system of trying to force the two events into one and rewarding designs and ideas with free upgrades/more cards etc. is really just a poor attempt and forcing a synergy under existing conditions.
To summarize, until the infrastructure exists that would allow new card designs to be directly used in War decks I will be opposed to a system that tries to force these two completely unrelated concepts into one event. If this infrastructure is developed however I would be very supportive of merging the two ideas. This lets the Scientists develop the weapons, and the Soldiers to find ways to utilize them just like reality. This is also the only true way to reward teams for having a purpose and vision for their war, instead of just designing a bunch of unrelated cards that really would be no use whatsoever to their team if they were real.