That wouldn't do much. Having a large down payment is great. It makes any financing contingency very strong, but I would have a hard time advising someone to avoid having one at all unless they planned to pay 100% cash. The terms of the standard contract may prohibit this anyway, without putting your earnest money at risk.
A buyer doesn't get a "cash discount" as it's all cash to the seller. The stronger the financing terms are, the more secure the deal is anyway. A 50% or more down financed deal would be as good as cash to me if the buyer had a strong pre-approval letter.