MoKelly - Thanks for the comments. I think it is a good question and will tell you what I have seen with regards to the initial install of the posts.
I also have an opinion on the structural aspect of the posts, but I would need to have an engineer chime in with the forces that come into play with posts and structural load/etc.
Once I get the post mounted on the base, I have simply nailed or screwed (using the structural simpson screws) through the post base to temporarily hold it in position. The post base has holes for this.
At this point, the post will stand up and not fall over unless I was to push it or put side to side pressure on it. I am able to drill screws into it from the braces I am attaching, so there is a desire to stand-up, but sure, if I wanted to I could knock it over.
The main purpose of the braces is to hold it in position (keep it aligned) until I can get horizontal beams installed between the braces. This will help tie the entire structure together and give it strength. It will then need some Y bracing/etc to prevent racking / twisting / etc.
My understanding of a post's job is that it is mainly taking a load from above and driving that force down to the ground or footer. For this reason, you want your posts to always remain straight. Bad things happen when the load is shifted from going straight down. The horizontal members, the ledger boards, the roof and collar ties all work together (or should) to tie everything together and give a structure strength.
Along the lines of your question, I will probably have my rear stall / lean-to posts cemented below ground to help further tie everything together.
I am sure there are people on these boards with a ton more knowledge than I. Please tell me if my thinking is off-base. Thanks.