Alkaline Battery for Boost converter for 1000ma current requirement?
Your boost converter requires at least 1.8V, so at a minimum you need two 1.5V cells. 600mA x 5V = 3W. Assuming 90% boost efficiency the battery needs to deliver 3.3W, which is 1.7A at 2V (1V per cell). 

A typical AA Alkaline will only deliver 200~300mAh at this current. However a 1.7A burst for 20 seconds per hour is an average of only 9mA, while the idle current will probably be around 25mA. That adds up to ~34mA total, so you should get close to full battery capacity provided that the battery contacts, wiring and power switch are also able to handle 1.7A bursts without excessive voltage drop (don't use a battery holder with coil springs!).

AA Alkalines have a capacity of 1800~2000mA at low current, so you should get at least 1800/34 = 53 hours or a bit more than 2 days of continuous run time. Will this be enough? For a device which is only used for a few hours per day it might be, but the user probably won't like having to replace the batteries too often. However one advantage of AA is that the user has the option of using rechargeable cells instead. Good NIMH cells such as Sanyo/Panasonic Eneloop can handle 2A without losing capacity, and 2 cell NiMH chargers are cheap and readily available.