Does including non-alphanumeric ASCII characters which do not require escaping or url-encoding such as
:@!$()* in URLs have any effect on SEO?
No- not generally. These have no specific search value in normal cases with some exception.
Programmers use word boundaries to separate terms of value in a string and would normally only use special characters if they have meaning. Special characters have no value when making text search matches except where there appears to be a special meaning. For example, an e-mail address or a phone number, etc. Special characters carry no weight and are not specifically used in semantic search as they are not part of a recognized term. Again, there is some exception for search intent in that search engines have to recognize using agents specific search intents for cases such as the ones I mentioned and a few others like it.