If you were flying SV-SV or connecting to SV, it would be a qualified yes.

Don't know which terminal EW uses but (having transited JED 2x recently albeit both SV-SV). If EW uses the same terminal as SV, there is a connection desk but it seemed very undermanned (early/mid evening arrival both times). IIRC, the sole person (airport/security, SV, handling agent, I do not recall) just checked our onward SV BPs before we went through security and up into the central departures hub. Be aware that it can be a long walk to this connection point (terminating pax also go here for the shuttle to immigration). To add to the misery of the last transit, the incoming flight arrived at a jetway gate at the new terminal, but at a domestic one so had to be bussed to some arrival entry point in the terminal (took longer than it should have), and connecting flight also required bussing to the hardstands close to the Hajj terminal (long way from the new terminal).

You would need to be eligible for KSA VoA (or have a KSA visa) at any rate and would not count on making the connection if you cannot get your return BP in advance.