im based in the UAE - i dont think i have been asked to or submitted my Emirates ID (in your case iqama) in my application so far... its only passport and passport pages which is required.
however, if you are legally not permitted to work in KSA, that might be a problem... so if you ask me i would avoid as far as possible to send anything related to iqama which says not permitted to work.
now there is another issue - you will need to submit copies of your visas and stampings in your passport, if on your residence visa it says not permitted to work - i can forsee that to be a problem also... whether you can write an LOE convincing enough for the immigration officer to rule in your favor - thats a different story...
i'm not saying you will be rejected, no... but i'm saying that could be a problem.