You receive through the post some great opening chapters. There's a space on your list, and this author might be the one to fill it! With the thrill of potentially having discovered a wonderful new author running through your veins, you call up and ask if they could send the rest. No, they answer. It's not written yet. Oh. Disappointment starts to set in. When will it be ready? In a few months. Oh. Then, a few months later, you receive the rest of the manuscript. You vaguely recognise the name, remember there was something disappointing about them and, with a grudging feeling of anticlimax, start to read. Worse, you then realise it's in a similar style/genre to the author you took on two months ago, and you don't have room for two novelists of that type. You put the manuscript aside.
If that isn't enough to put you off sending your novel out too soon, then I'd suggest a couple of other ideas that might, coming from a writing viewpoint. You've written 40,000 words. A novel is usually 80,000 - 100,000 words. Is it not possible by the time you come to The End you may:
a) have improved your writing style with regular practice so the beginning is now not as good as the ending.
b) have changed your original ideas, so the beginning you started with is no longer appropriate.
c) having written the whole thing, you've now got a much better idea of where you need to start.
I'd also add that I think it's much easier to write a synopsis and covering letter when you've written the whole novel and know exactly what it is you're trying to sell. In other words, the answer to the question is no!