If I don’t hook up to the OSSC, it will still display on an HDTV, right? Just not full screen?
Depends on what you mean by “full screen”, which could mean either the traditional 4:3 aspect ratio or “fills the screen”. I believe it doesn’t force any specific aspect ratio, so, like BuckoA51 said, it’s up to your TV to control the scaling and aspect. Most retro console content is going to be in 4:3, so you’ll want to play it like that, and you’ll only ever want to have it horizontally stretched to 16:9 if the game has a widescreen mode and you’ve enabled it.