I would have to say, yes, it does, but as evidence, one looks not at the scenario described of rolling a snowball down a hill.
Instead, in a snowy area, after a significant snowfall and, especially, if it leads to a cancellation of school, go outside and observe children and/or adults building snowmen/women.
How do they build the "snowballs" that are the body parts? There is an initial mounding of snow to create a ball, but to build it into much larger snow boulders, one simply rolls the ball around in the snow, and it increases is size as it picks up more snow from the ground.
YouTube: How We Build A Snowman
The reason why this happens is because snow will stick to other snow because of slight melting. The pressure of hands pushing the ice crystals together or the weight of the snowball pressing down onto snow on the ground causes slight melting at the surface, causing the crystals to stick together. So, if you have really light, fluffy snow, and brutally frigid temperatures, snowballs won't pack very well, and certainly would not accumulate just from rolling onto more snow.
The reason has to do with why snow sticks together in the first place. Snow is basically ice crystals , and when you pack the crystals together, you need to apply enough pressure with your mitten-clad hands to get some of them to melt.
LiveScience: How To Make the Perfect Snowball
This concept obviously applies to larger snowballs as well, which are the foundation of my "snowmen" scenario.
First, let's talk about the snow. "Snow can either be too wet or too dry," points out Dan Snowman, a physicist at Rhode Island College in Providence. Scientists actually classify snow based on its moisture content - the amount of free water relative to ice crystals - not to be confused with the amount of water the snow would produce if melted. Snow comes in five categories: dry (zero percent free water), moist (less than 3 percent), wet (3 to 8 percent), very wet (8 to 15 percent), and slush (more than 15 percent).
By that scale, moist to wet snow is ideal for snowman building, according to Jordy Hendrikx, a snow scientist at Montana State University. Dry snow is like a loose powder with particles that don't stick together very well, while slush is too fluid to hold a shape. "You can think of free water as the 'glue.' You need enough to stick the crystals together, but not too much."
Smithsonian Magazine: Do You Want To Build a Snowman? Physics Can Help
As far as the actual phenomenon of snowballs rolling down a hill, there are probably too many variables in terms of weight, pitch of the hill, initial velicity, moisture content, etc for me to properly find comprehensive analysis that in the space permitted, but most probably the answer is "yes, under the right conditions" for that, as well.