I see what you are saying now. Yes, that would give you more strength. Do you need it is the question. In my opinion, I do not think you do for a lean to that is securly attached to the existing building. I forget what you said you where using for your rafters, but if it was me, I would go with 2x8's or bigger.
I would also suggest you reconsider resting the rafters on top of a header, or a beam. For the walk through door, you can get away with a shorter span, and less wood above it to squeeze in a walk through door as long as the rest of the wall was properly sized. Given the spacing of your rafters, you might not even need a header over your doorway.
How far apart are you spacing your rafters? If at 48 inches, you just need a post under each rafter and the weight of your roof would rest directly on top of the posts. That would be the strongest of all possibilities.
Looking at your drawing, you have a lot of rafters. Are you going to shingle a 3:12 pitch roof or use metal? Shingles should never be used on anything less then 4:12, so metal is a much better choice. If using metal, you can space your rafters out 4 feet and use 2x4's on the flat for your purlins. That makes it really easy to find when screwing in the metal too!!!