Typically TPG's will only attribute a Morgan dollar (assign the VAM number to the label) if requested and not all TPG's attribute all VAMs. Some will only attribute the Top 100, Hot 50, Hit list 40 and a few assorted others.
Yes as all Morgan and Peace dollars are VAMs only some are worth a proemium, and even less are attributable by the TPGs ANACS will do any VAM as far as I know, PCGS and NGC only do certain ones from the TOP 100, HOT 50 and Hit list 40 along with a few Klimpton Clashed varieties. Most serious VAM collectors don't always care about the label having the VAM on it or not, while others do.
"Buy the Book Before You Buy the Coin" - Aaron R. Feldman - "And read it" - Me 2013! ANA Life Member #3288 in good standing since 1982, EAC Member #6202, NBS Member, 2¢ variety collector.