No, the point of Copyleft is for you to not restrict the freedoms you got when you used the software when distributing it to others. You can use Copylefted software in any way to your heart's content in combination with whatever other software you want, you can just not distribute it using a more restrictive licence.
This level of detail is incidental to my point, hence roughly speaking. Even
the GNU folks summarise copyleft essentially as I have. [0]
Also, your account of copyleft is still incorrect. It's true of the GPLv2 and
GPLv3 licences but not true of all copyleft licences. The AGPLv3 licence, which
is the one relevant here, doesn't apply only on distribution.
edit I think I was mistaken in putting propagate to code that is input to the linker, though. As lokar's comment points out, it's instead about the output of the linker.
