Do not use pressure treated wood. It is typically a soft wood like pine and will not give you the needed strength for a pulpit. Plus, it is not going to weather as well as teak or Ipe.
Suggest you go with teak or Ipe. You should wipe the glue surface with acetone prior to layup. This will eliminate the residual surface oil.
As far as adhesives, I would use either Titebond II dark or Titebond Polrurethane. Both pass type I water tests and are suited for outdoor exposure.
If you want, you could use a stainless threaded rod and hardware to add additional structural strength. Drill holes through all wood sections and use the rods and hardware (nuts, washers)to hold the sections together. The holes on the outermost wood sections will have to be large enough to accomodate the hardware and deep enough so that you can plug the holes with a wood plug after assembly. If you decide to use rods, use either two or three depending upon pulpit length.
