no, not every request. only those that don’t exceed `ndots` number of dots, typically 1 for unix like OSes. so google.com will not have fritz.box appended
Just checked, systemd-resolved doesn't even support that behavior anymore[1], so any multi-label FQDN will get resolved without appending the search domain.
So that's still a mess, but no mess of "rip apart the entire home network right now".
This is not true for Windows unfortunately. Even a lookup for google.com will have fritz.box appended. I added a screenshot to the article for clarity.