I'm aware that most people favor Deus Ex over Invisible War and don't deem the latter a worthy successor, but my question is this:

Is it possible to play Invisible War as a standalone game without having played Deus Ex GotY, and without prejudice? Will I be able to understand and enjoy what's going on without prior knowledge of the setting and story? Will it spoil Deus Ex for me if I play the games in anachronistic order, or will it make me enjoy Invisible War and appreciate Deus Ex more than the other way around?

I'm asking because I currently have problems running Deus Ex in a satisfactory way, and also because I read that Invisible War is kind of dumbed down and at the moment I'm actually more in the mood for a simple and short action game than an in-depth epic RPG.

Thanks in advance for any advice and recommendations!

Not really. In fact, I think it's better to play it first, because of the giant disappointment factor introduced if you played and enjoyed the first one. However it will somewhat spoil the ending(s) of the first one (since they didn't make one ending canon and somewhat merged them all together).
Also, with Kentie's launcher and other stuff (check the sticky) the first game is perfectly playable on modern systems/hardware, and it looks great.
Also also, get texture pack for IW. The game looks SO much better with this (google for "DX-IW Texture Pack.exe" about 140 MB size).

The issue I'm currently having with (the GOG version of) Deus Ex GotY having is sound-related, I don't know if the mods would change that. But thanks for reminding me to try them!

How big of a spoiler is Invisible War then? Does it spoil some ingenious plot twists at the end of Deus Ex, or something that is more or less predictable and/or not that essential to the enjoyment of Deus Ex and its story?

Never mind, I just installed Invisible War and it's lagging on my system, so I guess, at least at this point, the Deus Ex series is not meant to be played by me, heh. ;)

Not that big. Just the ending(s).