If you can see scan lines or pixel structure, then you are not seeing what the original picture was intended to look like.
If you are familiar with digital audio reproduction (CDs), then know that the principles are nearly identical. On a CD, the music is represented as samples spaced 1/44100 second apart. There is no information on the CD about what the music is supposed to sound like in the "gaps" between the samples. So somehow those "gaps" have to be filled in.
If you were to try a simple approach and hold each sample out for a full 1/44100 of a second, you would sacrifice sound quality, particularly in the higher frequencies; and a significant amount of harmonic distortion (though all of it in the inaudbile range, I'll grant) would be introduced.
That is what you're proposing to do with a video signal by expanding the width of the CRT beam. The impact on the video image would be the same as well: a loss of high-frequency content and the addition of distortion in even higher frequencies. Since image "sharpness" is communicated by high-frequency content, you will have an image that is "softer" than it should be.
Back to digital audio. The proper thing to do is to interpolate the signal to fill in the blank spaces between samples. In other words, the sound to be played in the gaps is computed from the samples that surround it, and their neighbors, and their neighbors... Shannon theory tells us exactly how that interpolation should take place. Unfortunately, in practice, it is impossible to perform perfect interpolation, so CD players pull all sorts of tricks to come close.
One common technique is to oversample the digital signal by computing intermediate samples to place in between the existing ones. When that's done you have an audio signal whose samples are, say, 1/88200 or 1/176400 of a second part. If these intermediate samples are chosen carefully, then the subsequent interpolation or filtering that is needed to finish the job is a lot easier to accomplish. In fact, our ears probably would naturally do most of it.
Oversampling is precisely what video scalers and line multipliers do. As the amount of oversampling increases, the scan lines or pixel structure become less visible. The natural filtering that occurs in the CRT, the lenses, and our own eyeballs help us to complete the illusion of a great picture.
So yes, even if the DVD only has 480 lines of resolution, the image can seem sharper can help to display the image on a higher-resolution device, as long as the scaling is done well.