What you need is sinusoidal current drive.
In other words, you have to treat the motor like a traditional brushless motor, rather then a stepper. This requires pretty specialized stepper drivers, and is not simple.
A simpler alternative might be to try microstepping the stepper motor, but that won't get you perfectly smooth rotation.
Really, for situations where you need extremely smooth rotary motion, a stepper is really just the wrong control system. You should use a brushless AC motor, or at least a brushed DC servomotor.
Here is a decent white-paper on stepper drive modalities, with some contrasting to AC synchronous motors.
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
YES
But you would have to add pulleys and belts made for steppers to reduce the ratio like 64:1 because a stepper may have 64 poles /rev as full steps while a BLDC might be 2 or 3. Then you may have to adjust holding-current to limit heat rise.
The gearing ratio depends on diameter ratio but can be cascaded and made to standard loops of belt or any linear length with end stop switches added.