Probably. We routinely lyse cultured cells by bead vortexing. You don't need a fancy bead beater. Put the cells and media in a 50 ml falcon tube, add a bunch of sterile 3mm steel BB's and vortex on high for a couple minutes.
We do this to isolate intracellular bacteria that we grow in the cells. Works great.
if the cell has a wall you are obliged to put after the lysis solution a glass beads and vortex. If no you're not obliged to put glass beads. For the lysis solution, you can used diffrentes solutions such as HEPES lysis, CYtobuster buffer, NaOH ....
It will woork but I guess it is a bit overdone. Most cells can be lysed by buffers or the use of trizol and bead mills will not dramatically increase the yield of RNA and in case of DNA preparation I would be even more careful to choose the right conditions.