Yes. The major scale in always based on the tonic note of the chord. For instance an Am chord is based on an A major scale, a Bm7b9 is based on the B major scale, a G7sus is based on the G major scale. This is always true regardless of the song's key signature. So if the above chords were played in a song's C key signature they would still be based on the A, B, and G major scales. Understand?
PS - that was a good question to ask.
{edit} Think of it like this, The first letter you see determines the major scale that the chord is based on. I say first because you may see a Gm7/F, or any other slash chord, and the second letter is only for the bass. For instance a C, C/B, C/A, C/G are all based on the C major scale.
I think I'm getting this. No matter what type of chord we are talking about, to decompse it to its individual notes you use it's major scale with the table I posted above that specifies its "formula"; 1 - 3 - 5 or 1 - b3 - 5 or 1 - 2 - 5 or whatever it might be.
And you read my mind regarding the
key of the song which was my next question. You still use the applicable major scale no matter what the key of the song is. So if an Am chord is in a song in the key of Am:
1=A, b3=C and 5=E.
And if the song is in the key of Bb (or any other key) an Am chord would still decompose to
1=A, b3=C and 5=E
And regarding the bass (or slash note), that is not a chord but a note, and a bass player would simply play that as-is.
Is all this right?