I don't have the answer, that's for sure; but here's some simple test results.
I created two Search Channels both searching for FIRSTNAME and LASTNAME (and I mean that quite literally
On one Search Channel I pre-clicked "Advanced syntax" and on the other Channel I didn't. Then I compare the two Channel Files using open source directory/file compare program WinMerge
There are a few different lines such as "ChannelGuid", "LocalChannelId" and several lines whose data is a timestamp. The "EscapeSpecialChars" line is the key line; it's got a value of "1" in one Channel file and "0" in the other.
Opening the Channel Properties of either Channel and toggling the "Advanced syntax" setting seems to toggle the value of the "EscapeSpecialChars" line and only the "EscapeSpecialChars" line.
So in my 2.4.1 Professional installation, everything seems to be working as it should; but I admit this is not a real world test on new-feed-item Search Channel results so maybe there's something else at play.