You have to make the RHS executable, by adding a /e modifier, and do the check there. I think this will do for your case:

s/(\$\w+)/exists $variables{$1} ? $variables{$1} : $1/ge;
[download]

but personally, I'd remove the '$' from the hash keys, and go for

s/(\$(\w+))/exists $variables{$2} ? $variables{$2} : $1/ge;
[download]