That's an interesting question regarding the mechanics. I cannot assure you 100% that being good at cubing doesn't give you an advantage, but I can assure you that I tried to eliminate that issue (the best I could) with my gamedesign decisions:
1) the cube is always scrambled after each action;
2) the competence (amount of moves you can make) is actually small (3 at best without "help");
3) you only need to care about one face (the challenge one);
For those reasons, I think that knowing how to do the Cube won't help much. Knowing the Rubik solution would help you if you needed all the faces put together and you keep playing with it until the end.
I believe however that being good at spacial awareness could give you some advantage. But only in the beginning - after a few challenges and the help of the party, anyone will get the hang of it (I hope). That advantage is the same you get when you are "creative" and pull out some stunts in your roleplay.