Yes. Remember that the power of an SSD is not that it can deliver 500 MB/s sequential transfers but that it can read and write 4K blocks very fast compared to hard drives but these transfers will be way less than 300 MB/s anyways so no need for extending this limit. And Intel ports will be better than just about any SATA card less than $300 US.
Unless money is an overriding factor, I would spend a little more and get the Sata III drive just for future use. Also spend a little more for the next bigger size if possible.
In fact, SSD's, even Sata II ones are so fast, I would say to getting a bigger size is more important than going SATA III, unless you are a benchmark junkie.
A SATA III drive will wring every ounce of speed possible out of a SATA II port. They are being built on the latest and greatest controllers. SATA II drives tend to be built on last generation tech, and may not swamp your SATA II connection.
In my past experience, add in cards for new tech in older systems do not really give you the best bang for your buck.
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