I bought that camera and case and YES for sure. Even had room for an extra memory card, extra batteries and the cord to hook it up to my computer. Its a small case, but its a small camera! I love mine.
It should. I have a Cannon Powershot SD4000 IS. I compared it to the dimesions of the dsc-w670 and they are almost the same. My Cannon fits perfectly with a little extra room. If I was buying a case for the dsc-w670 , I'd feel comfortable with the purchse. (Also note that Amazon usually has an awesome return policy if you have to use it.) Think you're safe!
I don't personally belong a Sony dsc-w670, but reviewing its dimensions on Amazon, it turns out to be 3.9 x 0.8 x 2.4 inches, whilst the Canon Elph 110 HS (which I bought this case for) is slightly smaller, being 0.8 x 3.7 x 2.2 inches. That being said, I definitely think your Sony compact camera will fit in the case but perhaps won't fit tight in it, which is not a deal breaker. Conversely, it can be good, so you can easily stuff an additional memory card and an extra battery in the zipped little pocket. Hope this helps.