If you use an external SSD it will only occasionally invoke the internal HDD like a cold start (so it boots the OS) or caching data when browsing the store but that's about it.
The internal SATA speed is largely irrelevant, USB3 tops out at 5Gbps which is just a little under the 6Gbps of SATA-III and SSD's over USB3 out-perform the internal Xbox drive.
Unless that noise is absolutely driving you mad, there is little reason to stick an SSD in there but go ahead if you feel like it, it wont make any difference if the SSD is SATA3 and the interface is still SATA2.