I have the same issues as Old-Spider, but have to add that I found it relatively hard to follow your instructions. Also, I may have an idea what causes the difficulties. Let me explain...
First of all, you wrote...
Extract the rar file to Documents\My Games\GC3Crusade. Goto Mods folder and read UCP_Install.
There is no such file under Mods, but there is a file called UCP_Install.txt under Documents\My Games\GC3Crusade. Guess that's the one you meant.
There you write about Intrigue and Crusade. Being relatively new to GalCiv3, especially mods, I am slightly confused which one to follow as I own both addons (well, that's an issue on my side, of course). Anyways, the steps to go are almost the same and neither way really works for me as we'll see next...
I both cases, you say that I should extract a rar-file, which can be found under Mods. Well, there are no rar-files at all under said location, only directories. So, I skipped this step as I thought that the instructions may be outdated.
Next step is to extract the colour palette. Again, you refer to the games mod folder, where no rar-files are located. Still, there is a UCP_Graphics.rar under the root of your rar / under Documents\My Games\GC3Crusade, so I took this one. Final step is to extract that file to ...steamapps\common\Galactic Civilizations III\Gfx, which I did, but in said rar-file there's another Gfx folder. At the end, I am not sure whether I should extract the rar to said directory or whether I should overwrite the Gfx folder with that from the rar.
In the end, the game starts, but there are no Trek races available and no new ships. Just as Old-Spider said. Also, I can confirm that the Factions folder is empty.
Now about what may cause this issue: my guess is that it is rar-handling in 7zip. When I started to install this mod, I had a relatively old version of 7zip. As a result, the rar file seemed to contain only 2 png files in a Gfx folder, which is quite nonsense for a rar-file of several 100 MB. So I updated the program and on first sight, things might be fine. Still, I could imagine that there might be files missing when unextracting the rar.
I could give WinRAR a shot, but having modded Civ4 myself for a while, I suggest you switch to zip as it would be only a matter of time till the next user will get the same difficulties. At least, if it turns out that my guess is right.
Also, there is a program called NSIS that can created installers out of a script. This would ease difficulties with the installation and solve possible issues with rar-files. Well, at least for Windows users. I could help you with such a script, so you would only need to set up some paths to fit your environment and run the script. But to do so, I would need to have an exact set of instructions, the mods files and as a result a running installation.