For the straight shot, the pocket is much more than half obstructed because the real pocket width is measured center-to-center of two balls in the extreme left-right positions as they enter the pocket. On a pocket that would normally be called "two balls wide," if a full ball blocks the left half of the pocket, the pocket effectively becomes zero balls wide -- there is no margin of error. (The extreme left position in your shot would be for a shot that almost touches the 8 on the way to the pocket.)
Sometimes you can shoot hard and force the ball partly through the corner of the pocket -- this is a standard advanced technique. I think the best way for you to see if it works is to try it and see how far to the right you can shoot the object ball and still get it to go in. See if softer still works for the same line.
If you are playing on a table that rolls as badly as the one mentioned in another current thread, you might be able to shoot softly and let the ball curve around the blocker. This requires knowledge of the table, experience and touch. If it works, your opponent is likely to think you got lucky. In general though, I would play a partly obstructed shot firmer than average to avoid any roll-off if making the shot was the only consideration.
