For example would the following code penalize you in regards to SEO?
<h2>Singles events across the UK! <span>Including Bristol, Manchester, London, Birmingham & Newcastle.</span></h2>
Would the content inside the <span> tags be regarded as less important?
You can never be sure about SEO but the answer is no, it doesn't hurt the search engine rankings.
Span is not required in the header tag, unless for a purpose (when an author wishes to assign style information to a set of elements). The documents are being read by a machine which are fed specific instructions and structure to process the meaning of that content. It depends.
The tag on its own shouldn't, but be wary if you're setting the span to display: none in a deliberate attempt to hack SEO, you may get penalised.