Yes you leave the point of the system bonding jumper with both a grounded conductor and an equipment grounding conductor. Just like you would do with a system with a neutral conductor. The current carrying grounded conductor is just that a grounded conductor. The equipment grounding conductor is bonded to the grounded conductor at the system bonding jumper but from that point on is not intended to carry current except for abnormal conditions.
Bond that grounded conductor somewhere downstream you have the same violation and similar safety issues as bonding a grounded neutral conductor in a similar situation.
Are you going to ground a phase? If not then you must have ground fault detection and indication equipment. Either way you run a 4th conductor as an equipment grounding conductor to bring all non current carrying metallic components to the same potential.
Grounding a leg puts that leg at ground potential. All three legs of your secondary are floating free in reference to ground until you ground one of them. POCO does the same thing when they step down to your facility. A wye system or single phase with a center tap usually gets the neutral connected as the grounded conductor, but it could be any conductor. A delta system, we generally call the B phase the one to be grounded, but you can ground any of the three. And you must have a A/B/C designation in the first place before you can demand grounding the B phase. Now in a switchboard or panelboard they may say B phase primarily because it is the center bus, regardless of what you might call it at the source.