I haven't tried this for eukaryotic (?) cells, but for E.coli I pick clones off an agar plate, disperse them in growth media in 96-well plates and PCR analyse aliquots of those. The initial denaturation lyses the bugs and kills any DNAses, and it usually works. Admittedly, that's for high copy plasmids, but I don't see why it wouldn't work for adherent cells.
There are kits for DNA isolation, but if you don't need the DNA purified (for Southerns or whatever), why bother?