If the doppler shift indicated that the shift was to blue-violet on the spectrum, would the big bang theory explain the shift?

The answer is no.

Explanation:

The apparent change in the frequency or pitch of the sound is known as the Doppler shift. The light from galaxies and distant stars can be shifted in much too a similar extent. In the visible spectrum, as red is at the low-frequency end, one can say that light from a receding star is redshifted or is shifted towards the red.  

If the Doppler shift is towards the blue-violet end of the spectrum, the Big Bang theory would not be able to illustrate the shift, as explosion makes the objects to move out, and if there is a blue-shift, it indicates that the objects are moving in, that is, the opposite of the red-shift.