In the case of the PCB manufacturers who have bolted a PCBA service onto their offering, you can only ask, although I think PCBway's online tool lets you specify you will supply the PCB as the PCB section is optional, I would also expect the quoted price to change on review as it isn't asking how many THT joints there are (or any real detail) for instance. For every other service they would normally be quite happy to either source/manufacture the PCB themselves just as they can with the other components of the build. However if you are supplying those parts you should always make sure what you supply is compatible with the manufacturing process.
Edit. Interestingly playing with PCBways form, they charge an instant premium for handling parts you kit to them, I guess that's fair enough as it is more work than working with their own stock. But then again the odds on them stocking everything you want on your build seem remote.