So I have Morrowind already installed in my PC via the offline installler.

If I then choose to use the installer of Morrowind again while the game is already installed, does it detect there's already a Morrowind installed? And if it does can it "overwrite" the older installation?

It doesn't automatically detect it, you can for instance choose to install the game to different drives and directories.
If you choose to use the same place where the previous installation is, then it obviously does overwrite it.

Your saved games should remain as they were, although backing them up before re-installing is highly recommended.

I'm not sure about GOG installers, but some installers will check the Windows Registry to see if a game is or has been installed, and what the path is. If they find such, then they may check the version and then prompt you whether to reinstall or update. Usually game saves won't be overwritten, though an update may make them incompatible.

I suggest you try and see, with a game you have just installed but not played yet. It could differ from game to game though, as I imagine the developer has some input and it is not just left to GOG.