You can see it like that, yes, but saying "this wave is linearly polarized" is pretty much indistinguishable from "this is a scalar-valued wave" if there is exactly one possible polarization (linear, and along one specific direction) that the wave can take. All one-dimensional vector spaces, even if they are subspaces of some bigger space, are isomorphic to just the real (or, if applicable, the complex) numbers.
So, it's ultimately a matter of taste in semantics. Yes, you can call that 'linear polarization', but you don't gain anything by doing that (except possibly add a bit to a topic that can already be confusing on a first go). Since you don't really gain anything, people tend not to do it. That then allows you to imbue phrases of the form "waves of the type X are polarized" with the nontrivial implication that there are multiple possible polarizations that the wave could take, and it allows for a lot of economy in communication in the right contexts.