Unless you have a citation that says otherwise, anything I've seen seems to suggest that there is little difference in the high percentage of mentally ill/substance abusers between chronic/non-chronic homeless.
Just about every article I can find talking about substance abuse and mental illness in homeless specifically focuses on the chronic homeless so I inferred from that. A bit of googling turned up this non-scholarly article though that compares the overall rate of mental illness among homeless to that of the chronically homeless and found ~3x difference
