Typically, the term "accuracy" refers to systematic part of the error, while "precision" refers to the random part:
Reducing the ADC range (by lowering the reference voltage) will increase the resolution and reduce the quantization noise (which is not systematic*), thus improving the absolute precision. However, this improvement will only be visible if the quantization noise is dominant: if another kind of significant random noise (e.g. from AC on the power supply line) is present, the improvement in precision will not be noticeable.
Accuracy (aka trueness) may also get better depending on the internal properties of the ADC. Non-linearity and gain errors are (usually) proportional to the reference voltage, so those absolute errors will typically be reduced, while the offset error may often not change. The overall change in accuracy will again depend on which of those errors is dominant.
According to Wikipedia, "accuracy" can be used to describe a combination of both random and systematic errors, so when both precision and trueness are improved, it's not wrong to say that the measurement has better accuracy.
(*) - quantization error actually depends on the signal, but it's a very useful assumption needed for the additive noise model, which is automatically holds when this error is relatively small. When the quantization noise is large, artificial random noise (dither) is often applied to make the additive noise model work.