My input source is 3x1.5V alkaline batteries. 

The input power supply is then connected directly to a 12V voltage boost regulator. I used my multimeter to measure the current draw of my load and it reads 200mAH. (The multimeter is connected series after the regulator and before the load)

Question:
How long will my batteries last assuming they have a total capacity of 900mAH? And will the current draw be the same if I used a 12V power supply non boosted? (Assuming the voltage booster has an efficiency of 100%)

My thinking is that since the voltage is boosted, in order to maintain the same power rating, the current draw will increase, which makes the actual current draw 533mAH in this case. Please advise!!