Do more objects appear on sky in time?
No, the expansion of the universe appears to be accelerating. Hence distant objects get more and more red-shifted. Our horizon is shrinking instead of expanding. At the end, only galaxies which are sufficiently bound by gravity remain visible; this could turn out to be the Virgo supercluster.

More reading about the accelerating universe on Wikipedia, and on National Geographic.

Scientific background to the according Nobel Prize in physics 2011.