It doesn't make any difference if you have an unorthodox grip or stance when you putt, but two things are vital: your eye must be directly over the ball, and you must stroke the ball to make it rotate end over end.
You have undoubtedly noticed that manufacturers are now making putters more upright. This is to help the golfer keep his eye directly over the ball. Every great putter I have seen does this. In effect, his eyes act in the capacity of eyes for the ball. The ball can only "see" the line when your eyes are directly over it. If they are not, your eyes will see one line while the ball "sees" another, and I don't think I need to go into the results of that.
When your eyes are over the ball, you have a much better chance of stroking it accurately and imparting end-over-end rotation. End-over-end rotation means that the ball is contacted so squarely that it rolls "over itself," on the same vertical axis, there being no side spin as there inevitably will be when the ball is cut or pulled or mis-putted in some other manner. If a putt stroked with end-over-end rotation hits a corner of the cup, it will not spin off and will usually drop. Bobby Locke, that magnificent putter, daubs a line of Mercurochrome around his practice putting balls so that he can check exactly how the ball is rotating.
from CHICK HARBERT, Meadowbrook Country Club, Northville, Mich.