Running a stepper motor at under its rated current will affect both its maximum speed and torque (both holding and dynamic), though depending on the driver type, it mostly effects the torque.
Firstly, The stepper motor driver you are linking requires power rails of 7-30V. Its logic interface is 5 or 3.3v.
Furthermore, your stepper motor is 3.6 ohms per winding, so even with 3.3V rails, your motors are going to pull ~900 ma, which will cause power rail brownouts.
Fortunately, in this context, the stepper motor controller IC provides chopped current limiting, which is a technique which limits the maximum amount of current it runs through the stepper motor. Therefore, you can run the stepper motor you have off the wall-wart you have, a the cost of reduced torque.
In a system which uses current chopping, the voltage largely determines the motors maximum speed, and the current the torque. There is interactions, but they are fairly small in effect size (assuming you are not at extremely low voltage or current), proportionate to the effect of changing the relevant characteristic directly.
I urge you to carefully study the A3967 datasheet (the A3967 is the stepper motor IC the linked driver uses).
Furthermore, the designer of that stepper motor driver provides a fairly decent introduction into the concepts of how the device works here, which, from your question, I don't think you have really read. You should carefully read it before you hook anything up, lest you damage one of your parts.
Additionally, the stepper motor driver you link already has a voltage regulator, so you do not even need the voltage regulator you included in your post (SFE sku: PRT-00114).
See the schematic for the Stepper Driver Here. The voltage regulator is IC2.
That driver will work fine, provided you use a proper power supply.
The allegro stepper-drivers are current-limited chopper stepper drivers. As such, you only have to ensure the power-supply voltage for the driver is > then the rated voltage on the stepper, and you have set the current limit properly.
Basically, chopper-stepper-drivers actually modulate ("chop") the drive voltage to the stepper in real-time to maintain a fixed coil current.
The ratings for your motor are steady state. Basically, it says that if you apply 2.55V DC, 1.7A of current will flow though the motor coil.
However, the Allegro drivers don't apply DC, they apply a duty-cycle modulated square wave, which limits the overall power delivered to the motor.
Functionally, the driver will vary the applied voltage to the stepper to maintain a fixed current (it's not quite that simple, motor inductance is involved, but it's a reasonable simplification). As such, as long as you're not applying more then 1.7A of current to the motor, it will work fine.
Basically, the simple version is the motor ratings are basically constrained by the thermal behaviour of the motor. If you apply too much power, it'll get hot enough to damage the motor.
With the A4988 driver board you link, you can vary the motor current by adjusting the tiny pot, which allows you to adjust the motor power to whatever you'd like.
If you run the driver off input DC within it's operating range, you will be fine.
Best Answer
There are 2 approaches to driving a stepper motor.
The simplest is just to connect DC to each winding in turn, via switches (FETs, driver ICs). And in that case, use 4.8V (5V - switch losses) as you confirmed from current and resistance. This is fine at low and medium speeds.
If you need maximum performance, you'll find the motor's inductance attenuates short pulses, so running the motor faster reduces its torque. You can overcome this with a more complex stepper driver, supplying pulses at the recommended 12-24V, to maintain current and torque at higher speeds.
Each pulse is maintained at a high voltage for long enough to build the rated current in the phase, then it should reduce in voltage to the safe level of 4.8V for the remainder of a slow pulse or steady state. This reduction in voltage can either be timed, or achieved by monitoring and limiting the drive current.
So both voltage ratings can be correct : 4.8V continuous, and 12-24V for an optional boost to high speed performance.