G7alt is a shorthand notation for G7(b9,#9,b5,b13), i.e., G B Db F Ab A# (usually spelled Bb) Eb. If You lay out these as an ascending scale, you get the G altered scale G Ab Bb B Db Eb F (which has the same notes as the Ab melodic minor scale, but the root is G here not Ab). But there is no E in this scale, as alt usually implies a b13.
If the chord you want is G7(b9,13) then you can use the HW-diminished scale, i.e., 1 b2 #2 3 #4 5 13 b7 (an octotonic scale). For G, this is G Ab Bb B C# D E F (and it has a major 13th, E). The G HW-dim scale contain many triads: G, Gm, Bb, Bbm, C#, C#m, E, Em, Abdim, Bdim, Ddim, Fdim (but not Ab major), and tetrads: G7, Bb7, C#7, E7, Abdim7.
This way of using notes belonging to a given scale (or mode) to play over a given chord or harmony, is indeed how modes can be used in tonal music. The important point to observe, is that not all notes are equally important: some notes (the root, 3rd, 7th) outline the harmony very clearly, some others (9th, 13th) add color, and some (11th in chords with a major 3rd, minor 6th and minor 9th in minor chords) sound dissonant and should be used as passing tone (unless dissonance is what you want, of course).
Discussing this in terms of modes is just one way of organizing the notes that sound interesting with a given chord in the a context of tonal functional harmony.