Yes - BBQ sauce can be canned. And the method of canning (boiling water bath or pressure canner) depends on the acidity. Here is one example
of a BBQ sauce which is canned by the boiling water canning method.
I agree with the suggestion that you telephone your county agriculture extension office instead of just dropping in. Not all offices have home food economist that can help you and it may need to be referred to another office. A phone call can get your query (and recipe) directed to the right person - usually via email in a case like yours.