No. If you bought it from HP with the auxilliary SSD already installed, that is NOT the same as my setup. I bought a laptop with an ordinary hard disk and then I replaced the hard disk that HP provided with a Seagate Momentus XT drive that I bought and installed separately. The Seagate drive has a standard HD and an SSD integrated in a single unit with all of the support for the SSD caching built-in, so it appears to the OS the same as an ordinary hard disk.

You bought a laptop containing an ordinary hard disk plus a separate Intel SSD based on Intel's proprietary "Smart Response Technology" (SRT). SRT support is built into the Z68 chipset (on the motherboard) and depends on the Windows driver for that chipset. As far as I know there is no Linux support for Intel SRT.

You can probably install Linux on your ordinary hard disk but then unfortunately you would get no benefit from the solid state drive.