When “etc.” is used with a singular subject, such as in the following sentence, should the verb be singular or plural?
The battery, etc., is included.
While people may translate et cetera in a few different ways, they pretty much all have a similar form: "and so on", "and others", "and so forth", etc.
etc. hasn't been Anglicised in use so as to ignore other features of it's origin, so we generally wouldn't have:
So there isn't much of an argument to be made for treating it any differently to its expanded form. Therefore "the battery etc." is plural.
Putting aside quibbles over whether battery, etc. is in fact a valid construction (I have no problem with it), the correct verb form is plural are.
It's plural because the subject includes at least two things - the battery, and at least one other thing which is "similar" to the battery in this context (since etc. means and other similar things).
FWIW, it would vary according to the specific product being described, but usually the most significant thing about a battery being supplied is that the product can be used straight away, without you needing to purchase additional accessories. So if it was a microtape voice recorder, for example, you could safely assume "etc." meant a blank microcassette tape was included.