I've always wondered about conversion of files at photo finishers. When I give them my 5-7 MB JPEGs, I suspect that the computer reduces the size to speed up the workflow (escpecially with 4x6 prints). Some insist that it doesn't (most have no idea), but usually when I get back wide-angle underwater prints (with alot of empty space in the background), this area is full of obvious noise that wasn't there before. I assume that this is from compressing the file to reduce the size. By the way, I never had this problem with photo finishers until about 5 years ago when they started getting those "self-serve" touch screen consoles (I don't know what they're really called). Even our local "professional" lab has the same one as Wal Mart now.
You can do some simple tests on the effect of compression by just using your image editor program to crank up jpeg style compression really high and see what happens. My experience is that what happens is a softening or loss of resolution, not the addition of noise. At very high compression there will also be some compression artifacts ("funny stuff") that shows up at sharp transitions like the edge of a wall in a topside photo or a mooring line or edge of a hull in an underwater photo.
Reducing file size by resampling down to fewer pixels has very different effect -- that of pixelation.
If you start doing heavy compression using GIF then you will start seeing things like color banding caused by having too few colors in the palette.
But I haven't seen compression cause noise to appear in empty space such as underwater background or the sky on a topside photo.
I have quite often had noise "show up" in prints. When I go back and look at the file at 200% or 400% zoom level, I find that the noise was always there, but just not apparent at the normal "fit in the window" zoom level. Nowdays, I often check for noise by looking at sky or open space at a high zoom level and apply noise filter as needed. (This is particularly a problem at high ISO settings.)
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I did another test just out of curiousity .... I resampled a bunch of photos to 1024 x 768 and printed them to compare with a Walgreens photo sent online using their "faster upload" (which is about a 5x compression) and uploading it full file size as if I were going to make a poster out of it.
The 1024x768 resolution photo looked OK and didn't have any pixellation, so they obviously did a good job of upsampling, but it was noticeably "fuzzier" or lower resolution that the other two photos.
On my first test like this, I lost track of which one had use the fast-upload and which one was full file size, so I repeated by adding labels to make two separate files. I couldn't really see any difference in the couple of photos I tested. I still upload full resolution since it just delays the upload a bit.