Times a DC motor can be driven from pair of AAA 1000mAh
In theory, yes, but battery voltages droop with discharge and motors' current varies with load. Also note that the 1000 mAh capacity will be at a certain load current, probably less than 100 mA. The datasheet will give you more information on that. You might get away with this though since your pulses are short.

The energy in your cells is given by volts &times; ampere-hours = 3 &times; 1 = 3 Wh.

Since there are 3600 s in one hour that gives you 3 &times; 3600 = 10,800 Ws (J or joules but Ws suits our purposes here).

Number of 1 s cycles = \$ \frac {Total \ Energy}{Energy/cycle} = \frac {10800\ \text{Ws}}{1.5\ \text W \times 1\ \text s} = 7200 \ \text {cycles} \$.