I believe Blogger no longer has this problem: on a new test blog, flipping the switch appeared to have no effect on existing posts. However, my blog predates this change.
Googling yields many reports of trouble with this maleficent option. Some suggest a laborious method of disabling it: turn it off, then break paragraphs in old posts by hand!
Such advice was probably written before Blogger gained the export and import features, which are the key to a simpler but scarier solution:
Export the blog, from the "Basic" tab under "Settings".
In the "Edit Posts" tab under "Posting", select all posts.
Delete them all!
import the blog and publish all posts, again from "Basic" tab under "Settings".
It works because the export format robustly represents line breaks with HTML tags whether or not the evil option was on when the post was written. Take care: after I exported my blog, I got distracted by the recently added "Spam" tab under "Comments", and found a non-spam comment sequestered within. I freed it, but forgot to re-export my blog, so after I deleted all posts and imported my blog, the comment was lost forever.
The export format has also given me ideas for my script that publishes HTML posts via the Blogger Data API, which has a hard time preserving formatted source code. Unfortunately, frequent experiments have temporarily barred my script:
Blog has exceeded rate limit or otherwise requires word verification for new posts
I’ll try again another day.
Unfortunately, I belatedly discovered serious manual editing is still required. Permalinks have changed; they now put the day of the month in the URL. Restoring old entries generates the new kind of permalink, invalidating all existing links to old posts.