Q:

Will making the surfaces extra smooth increase friction?

If we make the surfaces enough smooth that all asperities are removed then the two bodies in contact may act like a single body making frictional force infinte. 
I know this is practically impossible but is this true theoretically? If not please tell where I am wrong.

A:

The answer is yes.
Two smooth surfaces would appear to reduce friction, and that is caused because air particles will always be present within both planes.
So, in earth, two metals surfaces slide smoothly due to such effect. But in space, lacking the air molecules that prevent surfaces to reduce their distance, two smooth metallic surfaces can get sticked forever, because, paraphrasing Feynman, in such circumstance, the atoms on each surface don't know which surface they belong to. 
That would precisely be equivalent to infinite friction. 

