Yes, of course you can use it however you like. But if you have an interest, you can learn the English teacher rule, then make an educated decision on whether to break it.
As you mentioned, wikipedia (and elsewhere, I suppose) states that a semicolon may be used to "indicate interdependent statements." I asked my English teacher mother about this, and she said that the key is that the "statements" must be *main* clauses--in other words, things that could stand as separate sentences on their own.
"In the 'interdependent statement' usage of a semicolon," she said, "you should be able to replace the semicolon with a period."
"Then why don't you, like, just use a period?" I foolishly asked.
"Because you want to want to emphasize the *interdependence* of the statements." I had to go over to the other topic to find the exact example that you were wondering about:
The example: With a capacity for gold standard one-liners like that, and in the absence (vaccuum really) of Henny Youngman; have you ever considered a career in television or on the radio?
"The main clause," she said, "is 'Have you ever considered a career in television or on the radio?'. The part before that is an introductory prepositional phrase--actually two of them conjoined by the 'and.'" She said that the book way of punctuating would be:
Usual Style: With a capacity for gold standard one-liners like that and in the absence (vacuum really) of Henny Youngman, have you ever considered a career in television or on the radio?
She said that the first comma is not needed (but don't get her started on commas). The introductory prepositional phrase ends after "Youngman," and this is normally separated from the independent clause by a comma. In modern usage you may omit the comma after a short introductory phrase.
She said that you could also turn the first part into a main clause, like this:
Alternative: You have a capacity for gold standard one-liners like that; so in the absence (vacuum really) of Henny Youngman, have you ever considered a career in television or on the radio?
Next, she said that the hyphen in "one-liner" is by the book, and she droned about a spelling error and something about polite society, but fortunately I had tuned her out by then.
