So the GOG team added a recommendation at the beginning of the game to pick "Roland MT-32 MIDI board" as the sound mode.

But when I do that, everything sounds like piano notes. Everything is piano. Even when I fire my uzi or throw grenades, it sounds like a piano. Ridiculous. I've had a great audio experience in "AdLib sound board" mode though, which is the setting I would have recommended.

Anybody had a similar or different experience in "Roland MT-32 MIDI board" mode?

It appears that you never booted up the GOG version, so allow me to clarify. Indeed, Roland MT-32 is an original in-game option, but the game never actually recommends using it. I'm actually referencing the autoexec of a DOSBox configuration file included in the GOG installer (dosboxCovertAction_single.conf). It displays the following message before launching covert.exe:
--
Suggested game settings:
Press 1 to select VGA (256 color)
Then press 5 to select Roland MT-32 MIDI board
Then select if you want to use joystick by pressing 1 or 2
--

Considering that DOSBox does not emulate the Roland MT-32 but rather redirects all MIDI data directly to the sound card, I find it strange that somebody at GOG thought it was a good idea to configure DOSBox to recommend this option despite this flaw.

So I was wondering if the piano-everything experience I have is just because I'm using a shitty on-board sound card or if other people experience similar results.

I don't think the problem is on your side. Roland isn't really an option.

Please, GOG, change the recommendation to 4 Adlib Sound.

Yeah, the problem is that mt-32 emulation sounds ok as long as it uses the default sounds of the mt-32. However, covert action reprograms the piano sounds to use as sound effects. The emulation just ignores the reprogramming instructions, and thus you get that problem. However, it does sound great with a real mt-32.

Just ignore it and use ad lib, which still sounds fine.