The board houses may have questions for you that may be difficult for you to answer, but theoretically you could answer those with AI and get fully assembled boards delivered right to your doorstep.
we're also building a design house around it to close the loop with fabs, handle DFM questions and eventually let you hit "order" and receive fully assembled boards!
Its maybe more hands on than you want it to be, but you mostly just need to supervise the work. But yes, the CAD outputs go directly to the JLCPCB ordering form, or whereever you fab
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.
Go look at the library, I can’t really tell you if it is constrained for your use case.