I can save a model out of Blender with vertex colors painted (re-opened it in Blender to make sure it exported vertex colors), but I can't seem to get 3DX to recognize that they are colored. I'm working with FBX files.

Doubt it. Iclone is game graphics tech. Baking it to uvs is necessary.
Vertex color is pretty useful for 3dprinting though. Love using it in 3dcoat and lightwave.

Is IClone engine closer to a raytracing engine or a real time game engine(older generation)?
Yes or no?

iClone is only limited if you want to do things with it that it is not designed for. It is very suitable for making films though; I use it every day for that purpose. And no, it is not a ray-tracing renderer.

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ICLONE does not have to mimic a game engine or a regular 3D software. It can bring in interesting features from different sources can maintain its own unique positioning.
Quick and reasonable quality Rendering with ease of Animation have been its strength and ICLONE must stay focused on them.
In that context, investing in Indigo [ matter of fact speedtree and Full Substance except for B2M ] has been a waste of the limited resource ( at this moment). ICLONE should keep fine tuning its animation capability and try to stay on the forefront.

Infact I was wondering if ICLONE could adopt HUMAN IK 2015 and introduce those fancy creature IK !
Adding extra lights was necessary ( does not matter to me as I am only interested in toon shader ).
The soft cloth and dynamic hair options were definitely desired features.

What we need next is UMBRA3D ( www.umbra3d.com )kind of technology to stabilize ICLONE and perform better.

[ Since ICLONE does not have many serious toon shader artists, I would not unnecessarily push the desired features, though there are so many to talk about....I will welcome when they come on their own. I am not in a hurry. ]

Lastly, if RL uses C/C++, then PVS-Studio ( http://www.viva64.com/en/pvs-studio/  could help them write a less buggy software.