How subjective is a 7th chord?

Going through the lesson "Let's test the formula, with the A7 chord"

Lisa uses an open 'G' , replacing the 'A' on the G string to do an A7.

If you kept the A chord intact and just added the 'G' from the high 'E' - would that also be an A7?

Thanks

Scott

Yes. Any chord with notes A C# E G is A7, no matter what are the strings used, and in which order the notes are.

thanks