Definitely having a really large down payment, like 50%, helps set you apart from someone who is putting down 5 or 10% and hoping for a loan. In our case, we were buying a place near the bottom of the downturn, and paying a bit more than otherwise because we were already renting it and we wouldn't have to spend time and money moving again, so the appraisal came in a bit lower than we had settled on for the purchase. Still got the loan because it was for such a small amount relative to the total equity. I have definitely seen real estate agents on both sides of our transactions recommend particular purchasers because they weren't dependent on iffy bank financing.
That said, DW and I play our cards pretty close to the vest even with an agent working for us, especially on a purchase, we don't want any hints leaking through that we COULD pay more but choose not to.