Unless I'm mistaken, that's not enough info to say for sure.
You need to know how much of a sustained amp output the battery can handle. A 1500 mAh battery is probably plenty capable of pushing that amount of amps, and if it's protected you will *probably* come to no harm in trying.
But without an amp rating, (or C rating), no one can say for certain. (watt-hour rating is useless...note that 3.7 volts * 1.500 Ah = 5.5 W*h...)
