That is not what it means, no. The Tooltip attached to it says:
Prevents the Search Form from resetting when clicking through on to individual search results (modifies permalinks).
If a page has had an Ajax results update, the browser back button will only keep the previous settings IF the computer owner has made settings in their browser to support that. It is not something, as a web designer, that you can control. As to whether any specific browser supports that, I do not know. I have seen it work on some and not others.
Generally, I do not use the ‘Maintain Search Form State’, as it can cause problems of its own.