Regarding acid-base reactions, how does one know when a hydrophobic base substance is fully protonated?
Yes, that is correct. 
As you add HCl, the pH will remain more or less constant at around 5, since in solution there is a salt of a strong acid and a weak base. 
Then when all the base has been protonated, the pH will fall rapidly. 

If you need to know how much insoluble base you have, it must be done through back titration. You add an excess of HCl to the sample and then titrate the remaining free HCl.