Yes, you can use any of the colors from the palette in any combination.
There is a 4 color limit per sprite. The 4th color is ALWAYS invisible, so essentially aside from the background color you have 3 colors to work with that will be visible.
In the case of Simon, you could use 3, or you could use up to 6, why? Think back to Megaman games. Megaman looks like he has 5 colors! Black outline, darker blue, lighter blue, skintone, and white for the eyes. How is this possible? Simple actually... They use TWO sprites.
Attached is an image with two diagrams.
In figure A, we have two sprites, simply assembled in game. The down side to this is you must make sure they are completely contained. You can shift them and arrange them as you please, but each sprite can't contain more than 4 colors on its own. This is a tricky style to use.
In figure B, we have three sprites. We overlap the shoulder pads and hair over the top half sprite to get more colors. Just remember, the more sprites drawn the more slowdown you potentially have. Likewise the NES does flicker sprites if there are too many sprites horizontally on one scan line.