Yes, you can replace the 1 TB HDD with the 750 GB Seagate.
You will probaly gain some speed by replacing an average laptop (power optimised) drive with a drive which focuses more on performance. Even if you ignore the hybrid part of the Seagate hybrid. (Mainly the 5400 RPM vs 7200 RPM difference).
I do not expect the Seagate to be much faster then any other 7200 RPM drive. This because the hybrids use a trick where often accessed parts are cached on the SSD. Often accessed is usually things like the OS, Firefox/chrome/thunderbird/.... etc etc. It traditionally does not include movies. (Unlike you are someone who watches the same movie everyday).
This means that the traditional way of a SD + HDD combination stores the OS and programs on the SSD, and media data on the large (slower, but cheaper) spinning HDD. Thus there is not more 'low hanging fruit' you can gain by adding a second SSD or a hybrid with a SSD cache.
You will still get the additional speed from a faster drive though. And same generation 7200 RPM drives are faster then same generation 5400 RPM drives.