This is good one! I like it.
So for practical purposes an answer to your question is YES, in can achive a superluminal average speed and reach Andromeda in your lifetime.
But strictly speaking, in an accelerated frame can not simply add distances measured when you were moving at different speed. So distance becomes non-additive. Hence you can not just divide the total distance by time.
To clarify, asking about the distance Da (in a rest frame of observer A) covered by observer B in his proper time Tb, then Da/Tb can be >> c, but as you see it is a clear mixture of data from different observers and frames.