Alright, recently I've started to study Music Theory, and as of right now I'm studying Major Scales.

I already know the basic Major Scale Pattern.

I have learned how to "name" the scales based upon their tonic notes, and what I've been wondering about is when wanting to "expand" beyond the pattern.

Alright, since the we know that the notes C Major Scale are C, D, E, F, G, A, B we see that there are no flats or sharps.

Therefore, if I wanted to expand beyond the pattern, could I play any of these notes (C, D, E, F, G, A, B) anywhere on the fretboard, but they still sound in key?

I'm pretty sure it would work because the only difference between the same notes at different parts of the neck is that they are at different octaves.

Also, if it works with C I'm assuming that it works with all other keys (take A - A, B, C#, D, E, F#, G#), but I'd just like this to be confirmed.

Thanks for the help.
Yes, but by accenting certain notes and intervals in different positions you create modes.