I don’t think so. That would mean the galaxies were expanding away from each other at 99.99999% of the speed of light just barely keeping ahead of the light until it caught up with us after 13 billion years.
The light we are seeing left that galaxy 13 billion years ago. If the galaxies are all expanding, as they say they are, then it is a lot further than 13 billion light years away right now.
I don’t know the answer right now. I will look into it some more when my brain is working better. Because I do now recall that it is not as straight forward as it might seem at first.
For example...
3.1 Redshift velocity and recessional velocity
3.1.1 Redshift velocity
3.1.2 Recessional velocity
3.2 Observability of parameters
3.3 Expansion velocity vs relative velocity
3.4 Idealized Hubble’s Law
3.5 Ultimate fate and age of the universe
3.6 Olbers’ paradox
3.7 Dimensionless Hubble parameter
http://en.wikipedia.org/wiki/Hubble%27s_law