Is it okay for a PhD student to devote substantial work time to projects the advisor is not involved in?
It really depends on the funding source.  

It is fairly common for researchers in industry to get a Ph.D. "on the side" as part time work away from their full-time job.  Many professors are OK with this because 1) an industry researcher often has more maturity in their approach to a subject than a student fresh out of undergrad, and 2) The professor is likely not required to provide funding for the student.  

A professor who is funding a student to work full time from their grants, however, will be rightfully angry if the student does not work full time for them.