I would say, without a doubt, yes. SATA-III has a maximum throughput of 6.0 Gb/s, while SATA-II has a maximum throughput of 3.0 Gb/s. If we take into account the fact that both use 8b/10b encoding, both buses max out at a reasonable 600 MB/s and 300 MB/s.
I personally have the 120 GB model of the OCZ Agility 3, and it is running on my motherboard's native SATA-III port. During benchmarking, I hit well over 500 MB/s actual transfer rate, so you would be limiting your maximum transfer speed with the SATA-II controller.
If you do wish to upgrade with a new PCIe SATA-III controller, please see my answer to this question, titled "Adding a SATA 6 Gbit/s PCI Express controller card?". Summarizing what I wrote there, let us assume you use a worst-case PCIe 1x controller card. Your maximum throughput would be roughly 450 MB/s, or 1.5 times what you have now.
Whether or not you notice the difference in those transfer rates depends on you as a user, and what your purposes for the drive are. Even if your drive was capped-out at 300 MB/s, it still has nearly zero seek time compared to a conventional mechanical hard disk, and that's what most users will primarily notice.
After the whole seek time debate (because lower is always better), it depends on what you have stored on the drive and what you use it for (e.g. bandwidth intensive tasks like video editing, or low bandwidth tasks like internet surfing). That itself will dictate whether or not the increased bandwidth is warranted in your case.