Given the subjectivity of the judging, I think that it will be possible for them to narrow the field down as quickly as they need to.
Now if the deadline isn't carved in stone, I'm sure they will feel better about giving the submissions their due on the first read through. But If the deadline can't be pushed back, and they do get 5,000+ entries that fulfill the basic requirements, then they'll just have to judge very quickly and harshly to narrow it down to a hundred or so that they can thoroughly consider.
This is why spelling and grammar are very important. If they have 90 seconds to make the first read-through (weeding stage) I'm sure the entry will go in the round file at the first sight of a typo or verb disagreement. If you've already typed up your submission and were planning on sending it out tomorrow, don't. Take the weekend to re-read it forwards and backwards and to get friends, family and strangers to proof-read it. Ironically, I think that they will be, by necessity, more harsh on the first round submissions than the second round 10 page treatments.