It seems pretty unlikely those would be used as a key signature for anything because of the way the notes would work out.

Like the scale starting on A#/Bb... in Bb it'd be [Bb C D Eb F G A Bb], but in A#, it'd have to be [A# B# Cx D# E# Fx Gx A#] to hit the same notes. And while you can write in a scale with double sharps (although I've never seen it in a key signature), I suppose, it's just a helluva lot easier not to have to.

Which is where the chord names things come in, at least some of the time (eg: the Bb chord), since chords are based on scales. I think some of it also has to do with the commonality of the note--if I remember right, F# (the name, rather than the tone) appears in more/more common major scale notations than Gb does, which might explain why that name gets used more.

(Note* that this is based on old and fuzzy memory of theory. If I'm wrong here, somebody let me know--it's the only way I'll learn.)

[*Pun intended]

One thing to consider is the key you are playing in. If your playing in a flat key, you are going to refer to that note as Gb. If not, it will be F#.

Example:

Key of E - the 2nd chord in this key will be F#
Key of Gb - you will refer to the first chord in the key as Gb

this is very simplified and doesnt give much theoretical explanation, but i think it will help you understand why and when a chord is referred to as a # rather than a b...

:) hope i helped, I apologize if there was any redundancy!

... i play songs in F# major, that's how they're written that's how i play, and when i play in the key of Bb i still consider it F# because it was like that when i learned