Short answer, nope.
Any none SW 3d imported file into SW will be a lump, mass, meaningless, no history, nada. SW has a feature recognition tool, but you're still not going to get very far with it.
This has worked:
Use Inventor to import & recognize the MechanicalDesktop 3D dwg. Save the Inventor ipt.
Have Inventor and solidWorks running.
SWK FeatureWorks needs AIV >= Ver 11 (2007) on PC to interpret features.
Open the ipt with SWK.
In general, simple parts will recognize features.
Complex parts such as molded housings will recognize small features, and have the most important shape as a base lump that will not solve. This is very frustrating to business today.
Solidworks will import AutoCAD solids. However, as Mark indicated, they'll come into Solidworks as imported solid bodies without features. Usually this doesn't present a problem since AutoCAD's 3D Solids operations aren't structured around history modelling anyway. Since 2007, AutoCAD has included some built in history to edit the constructing elements of boolean operations so that you can change the value of fillet radii or reshape a tool body if this mode is enabled but it doesn't allow for indepth parametric design. You can't constrain profile sketches or reorder features in AutoCAD so you're not really losing much when you import it as a dumb solid into Solidworks.
Once inside of Solidworks, you can use FeatureWorks to recognize/rebuild the solid. I disagree with Mark about it's usefulness. It's not foolproof at recognizing features and automatic recognition is a crap-shoot. However, if you go through an imported part systematically using featureworks, and specify what to recognize and how to group it, it saves a lot of time over remodelling the part from scratch and generally produces a more faithful conversion. Featureworks is included with the Professional edition of Solidworks.
The method John mentioned applies if you modelled the parts in Mechanical Desktop-which hasn't been Shipped with Inventor series since 2005. However, if you still have Mechanical Desktop installed, you specify the Mechanical Desktop Import in the DWG Import Wizard.and it will recognize MDT features. Regular analytic features like extrudes, revolves and holes will come into Solidworks as features. Surfacing operations and 3D text come in as dum solids.
Best of luck, let us know how it goes.
SolidWorks can use the DeskTop engine to do smart feature based imports if you have it installed on the same box. We have ~10 years of legacy MDT 5 / 6 / 7 data & switched to SolidWorks about 5 years back & most of our machines had both installs for several years so it was very common, even for medium sized assy's to open in SolidWorks & let it convert via the MDT engine.
This gave us smart, feature based, editable models with some features needing clean-up, but on complex models with a feature tree a mile long, it was a small price to pay vs re-modeling.
SolidWorks says 2010 / 2011 should still be capable but most of us are now on 64 bit OS's & AutoDesk still has a bridge to get from Mechanical Desktop to Inventor in the Suite they offer (MDT 9). Unfortunately the only way to get it seems to be to buy the Inventor Suite unless someone out there knows another way.