of course you can. and whatever way you cut a hotdog in half, you'll still end up with a sandwich.
It would be part of the open faced sandwiches family, so definitely part of the sandwich genre.
This past November, hot dogs have been officially (yes: officially) declared to not be sandwiches.
And by what office and authority, you may ask?
Why the American organisation, The National Hot Dog Council, of course! Seriously.
According to the council, hot dogs are "an exclamation of joy, a food, a verb describing one ‘showing off’ and even an emoji," and "a category unto its own" as well as "not just a sandwich." They expand, saying that calling it a sandwich "is like calling the Dalai Lama 'just a guy.'"
Of course, no matter what these twatty prats have to say on the matter, it's a fucking sandwich.
>unironically shitposting in every thread on /ck/