Do you need ceiling boxes when using 2x2 troffers in a suspended ceiling.

No a box is not needed as each fixture has a removable plate on top with knock outs for the cable connectors. Once the connectors and cables are in the plate, make up the splices, you will find the fixture power leads just inside, just fold up the wires and splices and slide the plate back on.

Very important, be sure the ground wire is spliced, and is connected to the green screw on each fixture.

In addition to this, per NEC the fixtures must be attached to the ceiling with approved clips.

And you will need to check with the local building codes, many require that fixtures in a suspended ceiling be independently supported and attached to the building structure.