Question: When playing guitar,especially improvising,is it best to think of the notes a actual lettered notes or Scale degrees related to a tonic ? Since the keys are easily movable , I'm thinking that its better just to know the degree you want to play and knowing where that is related to the tonic.

Answer: 
Guitar is a three-dimensional instrument, where you are almost forced to know things in multiple locations.
Here's something I think is of paramount importance: when you learn a tune on guitar, you should always practice playing chord and melody 

together. That way you really learn to link the two things together. 
It has to become almost automatic. Then when you improvise, you should be able to see (and play) chords at almost any time as you go by.
About note spelling when you play, I think it has to do with different areas of the brain. 
It's the same thing that happens when you speak another language. These are two different processes: one process is knowing and using that 

language directly, without translating it. The other process is translating what you say into your own native language.
That's what simultaneous interprets do. But they never do the two things together; always sequentially.
So when you play, you bypass the names and go to the heart of things. If you really know these things, you won't need anything else. 
If you listened to music for enough time, you would tell most chords by ear, as if I’m listening to a D chord on the radio I know it’s D. 
And if I can hear their quality, find them on the fretboard, and play them, what else do I need?
I think it would be better to think the scale degrees. 

For instance, let's say you play E (V) and then Am (i); if you think in scale degrees, then you will lead the notes that consist the V (E major chord) to the tonic chord (A minor). This way, you make the listener believe that there is some connection between the notes you play. They are two degrees of a scale.

If you only think the notes, then it might not give the best sound outcome (the chords might not sound connected with each other). 

The notes will be the same, no matter how you think them, but the way you think, does affect the sound outcome.