Yes.
Look at jlcpcb or other Chinese assembly houses. If you stay within their component library it is dead easy, just upload your gerber and BOM, and you can have assembled boards within a week or so. Slightly more difficult if they have to order parts for your BOM, but still not really that hard.
if I needed something on the board that was outside the component library of the assembly house, can I ship it to them? or have them arrange for it somehow? How constrained is the component library?
Any PCB assembler can help you source outside parts or accept your parts.
Go look at the library, I can’t really tell you if it is constrained for your use case.