Global transpose does work, but you might see inconsistencies in the enharmonics (Cb instead of B, or in II-V-I progressions for instance) but this is the case with transpose in song view also.
Remember the key you set in song view is for concert key (so the player knows what key you want to hear it in, 'sounding pitch') whereas the chords you are looking at are in the key for your alto (set in global transpose.)
If you only play alto, you probably only need to set global transpose once and leave it there.