There is no such thing as SATA2.
There are various features that were defined by committe known as the SATA II organization. There is no "SATA2" or "SATAII" specification.
So a more proper question would be, "Does my motherboard support SATA 300MBps" or "does my motherboard support NCQ". The answers to those questions are Yes, and Yes but only in AHCI or RAID mode, respectively.
However, there is no drive in existence that exceeds SATA 150MBps speeds from the platter, and NCQ has been demonstrated to actually slightly slow single-user performance in most cases (see SR's own benchmarks) so neither of these technologies are highly relevant.
I suspect what you're REALLY asking is, "Can I attach one of these drives that the reseller incorrectly calls a SATA2 device in my existing PC" and the answer to that is definitely Yes, because any SATA drive will work on any SATA controller, all features are backward compatible.