Graduate TESOL Units = Graduate English Units?

Hi Everyone! Long-time lurker, first-time poster.

I have a BA in English and an MBA (general business). I've been teaching English (composition) classes for DeVry and Axia College plus a buying behavior class for UC Santa Barbara Extension and a marketing class for a small independent school.

Long term I anticipate earning a PhD in Management and Information Science from Claremont Graduate University, but in the short term I want to give myself some additional leverage and ways to earn income. I have been looking into some graduate certificate courses in English and related subjects so I can teach at more substantial schools. I also realize teaching English to people for whom it is not a native language seems to be something in great demand.

My question is this: Would completing 18 graduate hours in a TESOL certificate program also satisfy the need to have 18 graduate hours in English so I can teach it for some additional schools?

I am also looking into programs in technical writing and stand-alone English classes from Stanford's Continuing Studies department. I would like to only take the TESOL courses, but am unsure if that will satisfy my need to have the graduate units in English (proper). Do the graduate courses need to be titled ENGL to count?

Thanks for your help!