I'm really interested in getting this game, but I prefer buying it here since, well, good old game. Does this version supports custom user-made levels like in steam?

Thanks! Now I know what I will get this weekend!

Sure thing!
If you or somebody else needs the paths then they are:

LINUX
<home_dir>/.config/unity3d/Apogee Software/Secret Agent HD/Gog/UserContent/Maps

WIN
C:\Users\<USER>\AppData\LocalLow\Apogee Software\Secret Agent HD\Gog\UserContent\Maps

Do you happen to know:
1. Where to find custom levels (is there some repository with .lvl files?)
2. How to play them to unlock the "Pillar of Community" achievement (complete 5 custom levels)? I tried creating some maps locally and then playing them, but it did not work.

1. Unfortunately, the GOG version has nothing like Steam Workshop integration. Crystal Caves HD has an online repository on Google drive but I could not find anything community managed like that for Secret Agent HD. Unless somebody knows better, you need to ask people to share their levels. Probably best to ask on Steam threads.
https://steamcommunity.com/app/1607670/workshop/
I do not think you can just download these :(

2. Apparently it is bugged and it should be fixed but I do not know more...

Thanks for the reply!