Zoom 1xp would not matter, only changing the scale would. If it is drawn full (as it should always be) scale, it will be full scale in the new drawing where you locate it and you can do with it as you please once there.
Whatever layers are on, whatever fonts are used, whatever everything that is included in your "capture" will be what you get in the new location.
Re: moving an object from Model Space to Paper Space
does the "zoom 1xp" apply to all of paper space, or just a viewport?
"Zoom 1xp" is to bring your "Layout (floating) MS" up to Full scale. You are scaling it to PS. You don't use it in PS or "Model (tiled) Space". And if your drawing doesn't fit on the screen after 1xp, then you have to scale up or down until it does. I've explained this in many other threads. I'd be surprised if you haven't read them all.