1. This is overly simplistic. What happens if your IO and logic are by necessity interleaved? Grab X out of DB, grab Y or Z out of DB depending on X's value, etc.? The whole thing just reeks of "ideal case".
2. This is overly complex. All that really needs to be said here is "pull out your pure code when possible". There's nothing special about F# to enable that. The logic in "tryAcceptComposition" is just a function calling other functions; you can do that in C# or even C. The only advantage F# adds here is the piping syntax, which to me only serves to make the code more obtuse. But I guess you couldn't write a three-part series about a single "extract pure function" op.
(This brings up an interesting thought: ReSharper should come up with a way to let you highlight a function and extract the "obviously pure" tidbits automatically).