Searching for the character "$" in the thread search function provides no results, as below.

I can confirm that a number of threads contain "$", both in text outputs and in code blocks. Other special characters seem to work, as below.
[asterisk]

= (equals)

That said, other special characters like #, @, and ! don't yield any results — it is likely that these are contained in my thread history. % does work though, as do ) and (. Perhaps it is worth comprehensively testing special characters as a whole.