Not if the key is C# minor. G#7 is the
(And btw, I think you meant "G#m7", which is the v chord in C# natural minor
This progression is a variant of what's known as the "Andalusian cadence" - because it's standard in Spanish flamenco - Am-G-F-E (E major, not E minor). I'm sure if you play that (2 beats per chord) you'll find it very familiar! It's not just common in flamenco, you hear it in pop, jazz and rock music too. (California Dreamin' is by no means unusual.)
(They strangely omit this song from their list.)
The V chord in a minor key is traditionally changed from minor to major in order to make a stronger cadence (resolution) back to the tonic. Eg, in key of A minor, using E major provides a G# "leading tone" to make it pull stronger back to A.
This practice results in what's known as "harmonic minor" (because the alteration has improved the harmonic function of the chords). The "A harmonic minor" scale is A B C D E F G# - but this scale wouldn't be used on the whole sequence (it doesn't fit G for a start), only on the E chord. Otherwise it would be natural minor.
(Just occasionally, you might find "melodic minor" being used on the E chord: A B C D E F# G# - but usually only in melodies, and only when rising up to the A note.)
A harmonic minor will also fit Am and F, and is worth trying, to see if you like the sound - the more you use that scale, the more "Spanish" it will sound - which I guess is not totally inappropriate for California!
BTW, capo on fret 4 will allow you to play the key of C# minor with A minor shapes - which is how they played it.