Can you actually get to the center of the universe?
Based on this site, there are over 40 named galaxies (though most appear procedurally named). Also, from the link,
According to game data manipulation, the procedural engine can generate up to 256 distinct-looking galaxies (using an 8=bit seed); galaxies after the 256th will start looking like previously generated ones.
From this, it seems like reaching the center of a galaxy will just send you to another. If everyone does go through the same galaxies in order, then an ending seems unlikely. Unless the developers expect the average user to explore 256 galaxies before reaching the "end," which I highly doubt (plus 256 is only the number of UNIQUE galaxies; there could be duplicates), I'd say there is no true ending.
To answer your question, though, at this time, no, it doesn't look like you can reach the center of the universe, just the galaxies.