In the past, i.e. a billion years ago, if the universe is larger than our observable universe, would there have been more objects in our observable universe that have now accelerated beyond it?
A billion year is less than 10% of the age of the Universe, in Cosmological terms it is considered as the nearby Universe. There is not much change observed in that time scale. As a reference the age of the Sun is about 5 billion years.
To day, as in the past, almost all the Universe is observable in the visible light and longer wavelengths. The part that is not directly observable is behind the surface of last scattering that corresponds at an age of the Universe of about 400,000 years. The surface of last scattering is seen now at millimeter wavelength as the microwave background radiation, behind that surface the Universe is opaque. This opacity effect is similar to the interior of the Sun, in the sense that we can observe the surface but not the interior because the Sun interior is opaque. That does not mean that we cannot learn about the properties of the Universe at ages less than 400,000 years, we know quite a bit about the early Universe as also we know about the energy production in the core of the Sun without having the possibility of directly observing it.
When you see the skies,you are actually seeing the past..for in the sense,the speed of light is constant and the distance of stars is millions of light years..so the phenomenon which is occurring now in the skies will be seen later according to their respective distance from our planet.. hence the answer to your question is that there can be either less or more objects in the sky. The actual no. is RELATIVE...