As mentioned, the Activity will decrease and, subsequently, you may be de-ranked depending on how many posts you delete. The good news is that the Merits will stay, so in the hypothetical event depicted in the OP, it would only be a matter of posting (and time) to recover the Rank. Bear in mind that Recoverable Activity would not be available as an accelerator to recovering Rank if you delete all your posts.

In broader terms, some people have managed to de-rank their account from Legendary to Sr. Member and even back to Newbie, as well as others have taken their Hero member account back down to Sr. Member through to Newbie.

The following link details 115 significant cases of accounts that have been de-ranked by deleting some of their posts (and/or them being deleted by the mods/self-mods):
https://public.tableau.com/views/BitcointalkMeritDashboard/De-ranked?:language=es-ES&:display_count=n&:origin=viz_share_link

The toll I account for is really of 630 cases, though the Newbies to Brand New are not really relevant and are likely a result of simply being nuked. Note that I only track merited profiles, so I do not have a clue to those cases that have been re-ranked having earned 0 Merits.