Dominant eye question!

I am a lefty but my right eye is my dominant eye. Growing up plinking I always shot left handed but I had a day of shooting sporting clays with the British Olympic coach and he said to switch to using my dominant eye and it really helped my clay shooting. 

Does a scope eliminate the need to use dominant eye?

Noob question I know but just starting out in scope shooting and need to learn. 
 
Here is a discussion that might help. http://airgunnation.dev/topic/one-or-two-eyes/. I can shoot both left and right handed so, yes a scope can easily be shot with your non dominate eye. I am right handed right eye dominate and shoot with both eyes open when shooting right handed. Left handed I just have to close my right eye to get a decent sight picture. Hope that helps, but alot of good discussion in the linked thread.