The amount possibly owed is very minimal, but I want to make sure I don't get a penalty for not filing. I will include the amount to cover the possible tax with the extension, but if there is nothing owed, it might not even be worth my time for follow up with a final return. Is that legit?
Maybe. Filing an extension does not in itself require you to file a tax return if you are not required to do so. But, be sure you are aware of that state's laws about whether it is required to file there or not. It may seem like you might not have to file on the surface, but it may actually turn out that you do.
When it comes to a situation like this, it is better to file. There is no penalty for filing if a return is not technically needed. There could be a significant penalty if a return is not filed when it is required.
And how much or little tax you owe is not the determining factor, but rather, does your income require you to file in that state or doesn't it?
Ultimately it will be your decision whether to file or not, and by paying along with the extension you are recognizing as much. But the state will still want you to file the return itself if you have a filing requirement.