Can I soak and rejuice the pulp that comes out of a juicer?
The water soluble parts of the orange are all already solved in its juice. So in mixing the pulp with water, you aren't leeching any new orange components. The result won't be orange juice by any stretch, just water which has washed the last drops of juice your juicer didn't get. 

If you drink your juice diluted (I prefer it that way: less sweet, less fructose, better value), doing it might provide it with a better diluting liquid than pure water. But it won't be anywhere near real orange juice for drinking on its own. 

If you want to get some more orange taste out of the pulp, you can try boiling the pulp, or using a different solvent like alcohol or a fat. All will produce something very different from true orange juice (a syrup for the first if you add sugar, liqueur with alcohol or an essential oil with fat), and the amount will be rather small. So probably not worth the work.