I am considering a conversion of my utility room into a pool side bathroom and flipping the W/D to the opposite wall. Can a washer, toilet, shower, and sink run off the existing sewer and vent pipe? Additionally, my house is built on slab foundation.

"Can a washer, toilet, shower, and sink run off the existing sewer and vent pipe? Additionally, my house is built on slab foundation."

Not if the existing washer branch is two inches. Most codes mandate a toilet branch be four inches under the slab and three inches for a second floor instalation.
You may use the old washer vent to service your new bathroom group but I can see a lot of jackhammering in the future for you if you don't have at least a three inch branch to connect to. Good luck, Tom

Thanks for your help. That has helped me with the decision as to what to do with my laundry/utility room and office nook. It just started a whole new gammet of ideas.