Being lazy and looking for a way not to have to recompile personal books on second computer, I tried a test:
1. Take a document, create a personal book for it, Build it.
2. Sync.
3. Go into your resources folder and find the latest .lbspbb file, copy and move a copy to a folder on your other Logos computer.
4. Open up Logos 4 on that computer, and Sync so you see the meta-data for the new pb file.
5. "Scan" the folder where you put the .lbspbb file. (Type 'Scan <folder>' in command box). The close and reopen Logos.
6. Open library up, find title - it's there! open it - it opens!
No more compiling books for the second computer?