Yep, that will work better than alkaline. 800ma-hr for NiMH instead of 750ma-hr for alkaline. The actual difference will be larger because NiMH tolerates high current loads better than alkaline.
I'm partial to LSD (low self discharge) NiMH cells. About $2.50/cell from China: or $4.00/cell from USA vendor: Four cells per flashlight would cost $10 to $16 per flashlight. For that price, I could buy an equivalent LiIon flashlight, and still have some money left over for a crude LiIon charger. Most of these: were $5 to $10/ea plus charger.
I forgot to mumble something about the leakage current. Because the on-off switch is usually in series with the battery, the "off" leakage current should be zero. Yet, the Duracell Durabeam Ultra 350 flashlights seem to be leaking some current. Therefore, my guess(tm) is that the flashlight is wired in a somewhat different manner. Since the purpose of this flashlight is to sell more AAA batteries, I wouldn't put it past Duracell to put something across the switch or use a different wiring configuration to produce some leakage current.