Let me ask a few questions that will get your answer.
Have you prepared all the documents? If yes then you do not have to wait for any documents.
Is all documents with IELTS ready and do they qualify for 67 points at least? Then you have the package ready?
Can you afford the Cost of the courier to send the documents? If you are preparing for FSW then I don't think spending about $50 on courier charges should not be a big amount.
So let us evaluate the situation:
1. You send the application on 26th June, It reaches on time, the NOC is in category you make it in the Cap.
2. You send the application on 26th June, It reaches on time, the NOC is not in the list, it will be sent back to you and there will be no problems.
3. You send the application after 1st July, the application reaches just before the cap is filled no problems.
4. You send the application after 1st July, the application reaches after the cap is filled then the application will be sent back.
So you have to choose the scenario and decide if you want to send it by 26th or 27th June or after 1st July. I am sending my application by 27th so it reaches there by either 2nd or 3rd July. Most likely the list would be out by 25th June or so.