Yes, it is designed for 2.3 volts and would draw 2.3 amps, with two major caveats.
First, if you use a step mode which includes a time where both coils are energized, you may end up with higher than 2.3 amp current, so you might want a more capable supply. However, the overall current limit may not be the winding - it may be the risk of damage to the magnets if the temperature or magnetic field strength becomes too high, and those effects are somewhat additive, so you may not want to supply full current to each winding. That's where a full data sheet would be helpful.
Second, the coil has only 1 ohm of DC resistance. Once you start hitting it with pulsed step currents, the inductive reactance of the coil comes into play, and it will have a higher effective total impedance. With only 2.3v supply, you will see less and less current as you increase the step rate. To counteract this, high performance drivers use a supply voltage up to many times the rated voltage, and use a pulse width (chopping) current regulator to limit the current to the desired value - usually by measuring the voltage drop across a fractional-ohm power resistor in the return supply to the drive transistors/FETs. Even many of the small IC drivers have this mode.