No, it would not violate the principle of special relativity, which proscribes information traveling faster than the speed of light. Let's call the farthest object we can see X. Let's call X's neighbor on the far side from us Y. The only way for us to get information about Y is for information to travel to X (at or below the speed of light), which would then influence X's behavior. Then, information about X's behavior would have to travel to us (at or below the speed of light). So, nowhere is information traveling faster than light. The only information we can get from X about Y is already "out of date"* enough that special relativity isn't violated.
*The technical term relativists use is "retarded," but be careful how you use it in everyday conversation.
EDIT: We can make a distinction between the theoretically observable Universe according to relativistic considerations, which is what I was talking about above, and the Universe observable with present technology and practical limitations. Getting sneaky like inferring about Y from X actually does increase the latter meaning of observable Universe.