No, because it's ridiculous.
First person shooters are a specific genre that came out of the waning use of "Doom-clone", describing those games with 3D movement and typical shooting elements.
You can say light gun games are first person, you can say they are shooters, you can say they are fixed or on rails. They won't be thought of as first person shooters to anybody interested in the hobby.
It's like saying Sonic the Hedgehog is a racing game because you are racing to the end of a stage with a timer. It's too far down a pedantic rabbit hole to be worth thinking about.