Instlled with the GOG installer.
The desktop shortcut looks like that Cathode character in a circle.
I'd recommend this to some of my friends so please make it install with the classic 2004 icon that looks like a gold-blue "U" in a tilted elipse.

Yes, I'm aware that you can change the icon and that it's already in the same folder as the .exe.
But I want my friends to have a slightly better first impression. It contributes to that nostalgic feeling.

Can it be done if the GOG's setup(...).exe got edited? Or is it a lot of work?

So the thing is, even with your idea in mind, it depends heavily on how well the old "U" icon scales. Many icons weren't made in mind for anything bigger than about 48 pt, if even that large. GOG's icons scale up to 256, if not bigger. (It's been a while.)

At the end of the day, it'd still be UT2004, so why should they care about an icon they'll see for a femtosecond?

1) First impression
2) More nostalgia

Some people care about aesthetics. Also, if someone else sees their desktop, either directly or via a screenshot, they might recognize that game. ... Not with the GOG's icon.

But if it's "not worth it"...
meh

It might be possible to unpack the installer, but I'd have no idea how to set the icon to go with the UT one by default. I think GOG currently uses InnoSetup, if that's a possible starting point.

Installing something does nothing with nostalgia, seeing and feeling the software is the nostalgia. Just set the icon after installing the game. At that point no one can tell if you have the CD, DVD, Steam, or GOG release, not even you if you wait half year lol.