Yes.
But, from a writer perspective, pondering what form it would take, (or essentially...is there one after all, particularly in narratives like sci fi in general and trek in particular) is particularly good when thinking about things like why we do and don't like characters. (is the lions share of the inner light technically fourth person, what about choose your own adventure books? Stories with a time travel reset button that voyager excels in?)
I think that's a meaningless question. Even aside from the fact that "fourth person" is at best an informal grammatical category in English to begin with, the bigger problem is that grammatical persons in fiction refer to
narration. It's about whether the narration is written using the pronoun "I," "you," or "he/she/they." So as
Idran says, it really only applies to prose fiction, something that's narrated throughout. Most film and TV don't have narration at all, or only use a little of it. And when they do use voiceover narration, it's almost always first-person, a character telling a story. I suppose sometimes they have third-person narration, like the
Star Wars opening crawls or the similar expository text screens in various other movies and shows. Third-person voiceover narration is quite rare, I think. (
La Jetee, the inspiration for
12 Monkeys, is voiceover-narrated in third person, and I found that quite awkward and ineffective, distancing me from the story.) But narration is only a part of some screen stories, not all of them. "The Inner Light" only has one line of narration, the opening log entry, and it includes the pronoun "we," so it's first person. The rest is not narrated at all, though.
I suppose you can apply the concept of "person" to the camera viewpoint, as in a first-person shooter -- something where the camera is showing us what a character in the story is seeing, like in several scenes of the Fredric March
Dr. Jekyll and Mr. Hyde, say. But this is more properly called a point-of-view (POV) shot. Most camera angles in film/TV represent no particular individual's viewpoint and would thus be considered omniscient third-person. I'm not sure what would constitute a visual analog for second-person viewpoint, since what we, the viewers, see is the TV or movie screen itself plus the room we're sitting in. I suppose it would have to be an immersive virtual-reality environment or something.
Still, I think that using "person" to describe cinematic viewpoint is an analogy at best, and an imperfect one. So I don't think it works to talk about "person" in prose and film simultaneously, as if they were interchangeable.