Yes, it will do that. See my 'fixing a muddy run' page (link in .sig below) for discussion of pros and cons of things to add to your run, and (perhaps more importantly) ways to start fixing the too-wet problem. Without a multipronged solution you are unlikely to get really useful long-term results.
Sand (or other aggregates) are useful BUT in my experience they disappear very quickly if added to an already muddy run. So if you want to get maximum bang for your buck (and for your *exercise*, which shovelling and wheelbarrowing lots and lots of aggregate is certainly good for!) it is really best if you can wait til the driest part of the year to add 'em. Otherwise you may be doing the same thing again next year.
If budget and workload are not a concern, my suggestion would be to do all possible diversion/drainage things (roof gutters, downspouts leading water *far* away, trenching around run, roof run if possible) and if that's not enough then put down some ag lime and cover it with 6-12" of safe tree-chippings for now. Then when the dry season (however 'dry' that is locally) arrives, shovel all that back OUT of the run -- you can use it as mulch on the garden, or till it into the soil in the fall for soil improvement in the garden -- and replace with a substantial amount of sand or other aggregate.
If you won't be able to remove the muddy chippings, I would be leery of putting them in, though. You can either put in a lot of sand (like 4-6+") *now*, in the knowledge that it will almost certainly be fairly short-lived, or just deal with the mud as best you can til dry season and THEN add your preferred type of aggregate.
Good luck, have fun,
Pat