Theoretically, yes, though those arguments don't tend to be the strongest. When the other side refutes, the argument becomes less persuasive and more chicken-and-egg.
The best values are the ones that are intrinsically valuable. For example, instead of the broad argument that national security leads to "other good things" and "other fundamental values," a better argument would be that national security leads to domestic tranquility/peace, which are inherently valuable (as long as you accept that war is not ideal.) Or instead of arguing that privacy is good because "achieving privacy means that you've already achieved a bunch of other stuff," you could make your point stronger by instead arguing that privacy is inherently valuable, or that privacy necessarily protects Human Dignity.
It's a much stronger rhetorical point to pick something specific, inherently valuable, and definitively tied to your side of the motion. "A vote for the negative is a vote against human dignity" will always be a stronger argument than "you should value privacy because general rights are needed to make privacy come about, so valuing privacy means you support that other good stuff by default too." See what I mean?