Nope. ALL grounding points should be tied together at one common point. Remember that if the antenna and it's components are grounded separately then that still leaves the potential for a difference in voltage drop between the antenna and the equipment chassis and since the two are connected via the coax cable or even the third wire in the AC cord depending if it is tied to the common point or not, current will flow on the shield of the coax back into the shack.
I see the new owners of Polyphaser pulled all their online info regarding grounding. Good thing I downloaded it before they pulled it. Hopefully it comes out here as a .pdf attachment.
Grounding points must be bonded according to the NEC(in the US), all ground rods and interconnecting conductors must meet the standard. If you are connecting an antenna coax and mast to an existing service panel ground the conductor can be no smaller that #10 AWG, but if you are using another ground rod for RF or station ground then the conductor between ground rods must be #6 AWG or larger. I wish I could find my NEC book, I am sure it made a difference if the grounding conductor was solid or stranded wire