You as BLS working in Los Angeles and/or Orange Counties, you're pretty much doing what the Fire Medic tells you to do. Whether you stay and play, or transport doing compressions will not be your call.
Now remember, they're largely teaching Stay and Play for cardiac arrests. If you find yourself first on scene (even if its an IFT and you have to be the ones to call Fire), you do CPR, stay and play on scene, till LACo or OCFA or whoever shows up. Work the patient where they are. (Though it is entirely permissible to drag a Cardiac Arrest patient out of a narrow hallway/off a soft lumpy bed/etc into a room where they're on a nice firm surface and you have room to work).
If you're dispatched to a reported Cardiac (Full) Arrest, bring your backboard with you to scene. If you transport the patient will be on the board. No need for C-collar, you're not doing Spinal restrictions, the board is to provide a firm surface to do CPR on vs the gurneys soft mattress (also easier to carry a patient out if you need to leave the gurney outside).
Hopefully thats more of a precautionary method if you need to do CPR after a patient who has ROSC codes again enroute. But just in case the medic decides to transport a working arrest, then yeah basically you'll be interrupting compressions to load onto the board, carry board to gurney, load board and patient onto gurney.
Someone will be "riding the rails", standing on the bottom rail of the gurney doing compressions while its being moved to the ambulance (or from ambulance into ER) and once again compressions interrupted to load/unload gurney from the ambulance.
Hopefully you won't actually have to take part in that procedure. When I was with McCormick working with LACo, we were definitely doing a lot more Stay and Plays vs loading and going with arrests, so hopefully short of any of the special circumstances some of the other posters mentioned, you won't have to do that at all.