Yes, it's important to descreen a scanned halftone image even though it's going to printed at the same size as the original.
In this answer I will assume that you are printing with offset or a digital printer which uses halftone screen. Many digital printers use stochastic raster and won't have the exact same issues, but likely something similar.
The moiré pattern you see on screen is the dissonance between the halftone pattern of the scanned original and the pixels on your monitor. It's particularly visible at uneven zoom levels like 33.3%.
Although it's the same phenomenon, it's not the same moiré pattern you will see on print. You can't really rely on just viewing your image zoomed out to get a proper preview of how the halftone dots will affect the final print.
The problem with having halftone dots in an image is the dissonance that will be between the halftone pattern of the scanned original and the halftone pattern of the final print.
When printing we can only print solid colors. To make tints we have to do some kind of screening. With a halftone screen a 300 ppi 8‑bit image are interpreted and turned into a 2400 ppi 1‑bit image for each channel with sharp halftone dots (these resolutions are commonly used examples).
You have a scan of the printed halftone dots, but there is no (common) way you can recreate the original CMYK separated sharp halftone dots which was used to create the print in the first place. Firstly, the scanned image is just a soup of RGB pixels and no longer separated into CMYK. No way to know exactly which channel each pixel represents. Secondly, the scanned image is too blurry to clearly distinguish each dot.
If you do send an image to print which contains halftone dots, the dots won't be printed "directly", but they will affect the printed halftone dots in a pattern that is most likely out of sync and create the dreaded moiré. The patterns will most likely have an offset, the frequency of the patterns will likely differ and they probably have a slightly different rotation.
Here I'll try to make a preview of how I believe an image with raster dots will look on print. This is a home brewed method I made, so take it for what it's worth. That said, I believe it gives a pretty good idea of what to expect.
First I apply a halftone pattern similar to the ones used for print:
- Scale the image up to 2400 ppi.
- Convert the image to some CMYK profile.
- For each CMYK channel:
- Copy/paste the channel to new grayscale document.
- Convert to Image > Mode > Bitmap using Halftone Screen with a Frequency of 200 Lines/Inch (common for printing on coated paper), Angle set to respectively 15 (C), 75 (M), 0 (Y), and 45 (K) degrees and Round shape.
- Copy/paste the bitmap image back into the channel it came from.
The result doesn't really reveal much. Just the expected jumbled mess of halftone dots.
I want to smoothen the image a bit to make it look more like a scan of a print:
- Apply Filter > Blur > Gaussian Blur with a Radius of 3px.
- Scale the image down to 25% size with Bicubic Sharper interpolation.
- Apply Filter > Sharpen > Unsharp Mask with an Amount of 75% and a Radius of 1px.
This looks pretty much like I'd expect the final print to look. The are some obvious problems with moiré and the overall appearance is noisy and gritty.
For comparison I've tried to sloppily descreen the image before applying the above method.
This looks way more even and smooth. Some of the details are lost (you could probably do a better descreening), but we don't get that same gritty appearance as before. I would prefer this result to the first.
Another reason for descreening an image is that you probably want to color correct the scanned image before print and having halftone dots really makes it difficult. Any correction will affect the edges of the scanned halftone dots and thereby affect the image in unexpected ways.
Furthermore, the halftone dots create the illusion of colors in a pattern where some of the dots lie alone and others overlap. If you for example try to change the hue of all reds you might only be able to target where the yellow and magenta inks are overlapping, not where yellow and magenta dots lie closely together.