Are watermarks constrained by the quality of the underlay video?

This may be a stupid question but I have to clarify it for my own peace of mind, so bear with. The good news is it's more or less a yes/no question for the FFmpeg/AV experts who know the answer.

Say I have a low-resolution source video eg. 320x240, and a PNG watermark image that was actually produced this decade, so at least double that resolution and high-quality.

If I use FFmpeg to overlay the PNG on top of the video, is it unavoidable that the quality of the PNG will be limited to 320x240 pixels, being constrained by the resolution of the video... or should it be possible for it to look sharp and high-quality (i.e. like it has all its original pixels) even while the rest of the video does not? If it's the latter case, then I'm probably just doing something wrong in my experiments.

It will be small & crunchy.

You don't even need to test this empirically. Your output resolution is 320x240, any & all elements within that will also have that maximum pixel count - or considerably fewer in the case of a watermark tucked in a corner.