Essentially you'll be a stand-alone domestic passenger on your Jeddah departure. Though I have managed lounge access (at RUH) on the strength of SkyTeam membership and an international to domestic separate ticket transition. Lounge entry staff can be agreeably low-key, especially with visitors to the kingdom: but don't bank on it!

So it's worth a try: show your in-coming boarding pass as well as the out-going one, keep your fingers crossed but be prepared to accept a no-go, Refusal wouldn't be the end of the world: the arrival procedures, baggage reclaim and checking in again will eat into your time - and there are cafés and things to do airside.