In the Minolta auto-focus era, yes older lenses will work properly with the newer Sony dSLR cameras. Older manual focus lenses will not however.
If a Minolta lens is marked, "AF" or "MAXXUM" it is A-mount and will work with the Alpha dSLRs (and the new E-mount NEX with an adaptor)
Manual focus lenses are indicated as, "MC", "MD", "Celtic", "Rokkor" or "Auto Rokkor". Don't get confused on that last one, "auto" means automatic aperture - not auto focus.