No, but using User Macros you could write your own and adding in the functionality.
You can find the VTL code for a version (I'm not sure how modern it is) for the code here: https://confluence.atlassian.com/display/CONF34/Writing+the+Status+User+Macro.
We wanted to do this and came up with a jQuery based solution. It works well for us, as the coding is hidden from users in a page template. The gist of it is to define the link you want to apply in the normal way, but inside a "div" element (thanks to the Adaptavist Content Formatting macros plugin). This div has its style property set to display:none, so is invisible when the page is viewed normally. The jQuery code looks for this link and applies it to a status macro, based on the text that has been set for it.
Why go to the trouble of making a hidden link in this way? Since it relies on the normal Confluence functionality to do this, I see benefits if the target page was to undergo a change of name. In other words, we're not hard-coding the link.
Here's some sample code. If you have the plugin I mentioned and the html macro enabled in your environment, then just put this directly into a test page and you should see it works nicely. Note - the link is put on the entire status box, not just the text within it.
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