There's no space for doubts at all. If it starts with $ then it's a scalar variable name. It's a very basic rule in Perl. Like any Perl tutorial would mention it within a few paragraphs from the start.

So then wouldn't that make $|++ the variable name?

Smokey, this is not 'Nam! This is <Perl>, there are rules!

'$' guarantees a scalar. Then it either alphanumeric id, or a single non-alphanumeric symbol. And the latter means you deal with a 'special' var which with 100% certainty has a documentation entry.