Yes, and no.
The Equipment Ground Conductor for multiple circuits is sized for the largest circuit in the raceway. Sized from table 250.122 for the largest OCPD.
250.122 (C) Multiple Circuits. Where a single equipment ground-ing conductor is run with multiple circuits in the same raceway, cable, or cable tray, it shall be sized for the largest overcurrent device protecting conductors in the raceway, cable, or cable tray. Equipment grounding conductors installed in cable trays shall meet the minimum requirements of 392.10(B)(1)©.
Additionally, the Code allows you to use the raceway, if it is metallic, as the EGC and save your money.
250.118 Types of Equipment Grounding Conductors.
The equipment grounding conductor run with or enclosing
the circuit conductors shall be one or more or a combina- tion of the following:
(1) A copper, aluminum, or copper-clad aluminum conductor. This conductor shall be solid or stranded; insulated, covered, or bare; and in the form of a wire or a busbar of any shape.
(2) Rigid metal conduit.
(3) Intermediate metal conduit.
(4) Electrical metallic tubing.
Lastly, if you have UF cable you don't need a raceway unless it is exposed to damage and it should already have an equipment ground wire in the cable.
Good luck with your project!