Switching a good stone woodburning heatilator fireplace to a gas log

Our woodburning heatilator fireplace with glass doors & blowers truly heats the better part of our 2000 square feet main floor. I am considering putting in a gas set but the local firplace dealer says I'd need to keep the doors open because it won't get enough air. If my wood burning fireplace gets plenty of air with the doors shut, wouldn't that also be enough to safely run a gas log set? And if my present firplace also puts out plenty of heat, wouldn't the gas log set also. The difference in the cost of doing just the gas log set venting thru the damper in the chimney compared to putting in an insert and reventing etc is a matter of thousands. Any help, ideas, suggestions would be appreciated
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