I got my first upgrade, as a lowly Silver, in a year when I used that "Virtual Concierge" to ask the Marriott Minneapolis to "do their best" to find two double beds, since we were traveling with a child, in a hotel that was filled to capacity for a convention I was attending (and we had snagged a Summer Sleepover rate way back!) Had a personal response in an hour saying two double beds were guaranteed, and a Concierge Level room waiting when we arrived at midnight the next day! Nice touch (and, I have to say an enthusiastic staff there throughout, for a hotel that doesn't always get rave reviews on the Web).
I suspect during conventions when rooms are filled with non-Elite members, it may be easier for relative lowlife like me to get an upgrade.
By the way, is there any distinction between Silvers who have stayed 49 nights a year and someone who just got a Marriott Visa Card, in terms of upgrade chances?