Can a wine press juice citrus?
Theoretically, you could use a wine, apple, or or other heavy-duty fruit press to press 10-20lbs of citrus at a time.  But you wouldn't want to.

Both the peels of the citrus and the seeds contain bitter and/or intensely acidic compounds (those essential oils WS talks about in the comments).  If you press citrus in any press that uses pressure on the whole fruit, then those compounds end up in your juice, making it taste bad.

This is why even juice factories do split-and-squeeze(video) instead of using straight pressure.  If this is something you often do, you may need to invest in an automatic-feed juicing machine.