A great question. The fact that we have no definitive answer is the reason our housing market is in doubt.
The lifeblood of our industry is sales. Predicting the elements which make it happen is what makes us professionals. The banks have made us doubt ourselves with all the fundamentals that once were easy to reply to. Thirty percent is a substantial amount of downpayment in any market condition. Yet as I have stated the variable response may be as confusing to you as to us. It could be challenged by an appraisal which would negate your scenario or your ability to qualify based on any number of requirements that change daily. Since you state the amount to be mortgaged to be quite negligible in the first place, they may simply refuse it on that premise.
As Anna suggested I will also kick the can further down the road by suggesting to shoppe around.
What a shame . A simple question that only keeps us realtors guessing. Good luck Brian