No. On the upgrade page, it says that "DIRECTV DVR models SONY SAT-T60, PHILIPS DSR6000R, HUGHES GXCEBOT and HR10-250 will not receive the 6.2 software upgrade at this time." That's the three S1 DirecTiVo models, plus the HD one.

If it's not clear, this is only talking about upgrading the DirecTiVos. The S1 SA TiVos have been EOL'd for quite some time now.