It will definitely help to have a passing score on Step 3 and even better would be to have a valid permanent state license in any state. I was never asked specifically asked about step 3 scores during the application process but all programs will ask for copies of Steps 1-3. I wouldn't wait too far beyond your internship to take Step 3.
I have given this advice in other posts, but it is wise to take (and pass) step 3 and get a permanent state license sooner rather than later. It is easier to keep a license than to get one (i.e. if something happens like a DUI during internship, etc. prior to your permanent application). Something like this could be a real obstacle for initial licensure.