Assuming 600mA is enough for the motor (should be!), you're good to go.

That's pretty much the only consideration. A Li-ion battery is just a special case of a DC supply varying around 3-4.2V, which means any "product" designed to work with such a battery is implicitly guaranteed to work within that voltage range whether it be provided by a $1000 bench power supply or 4 lemons in series...

Point is the "type" of supply is essentially irrelevant to the load (as long as it functions properly as a supply), except for how much current the load will try pulling out... So, as you'd expect you sure can replace a battery with any equivalent voltage as long as whatever that is won't blow itself up trying to match the current draw that was designed to be coming from potentially high drain batteries.

Just be very sure you have the battery chemistry right when doing this, because none of that will help you if you mix up LiFeO4 and LiPo/ion