Guess not.
If you remove a thread you remove all posts, thus as I said any other posts to that thread also go.
I see that "Remove" was a poor choice of a word here. Perhaps "Unsticky" would have been a better one.
But as David said or implied the quality of his sticky has nothing to do with the reason he is banned, so why loose that information.
My first thought was that it gives a negative first impression to newcomers. Most forums that I have been on have had "rules" or "FAQ" type posts written by the moderators. If you read them, and had a question, you could contact that moderator and ask. Then if the moderator needed to update the particular sticky, they could do so. In essence, the sticky was sort of a living document.
If the sticky is written by a banned member, newcomers may question how useful/appropriate the information is (because they won't instinctively know what the person was banned for).
As a side note rather than starting a new thread:
In the Forms category, there is a moderator by the name of
AprileC that shows up on the bottom of the page. Her profile says she hasn't been active since 2007 but there are visitor messages left for her (mostly questions) up until November 2010.