Did a little more research on this one.
There are 3 630's that were sold. 630, 630II, and 630 super, which causes some confusion. Earlier models used a thin ring piston, which has been replaced by a thick ring piston. They are all essentially the same saw. They all take the same jug and piston; part # 503517502, which is the thick ring design. This logic pretty much applies to the 670's as well.
Depending on which price list I look at, it is either $205 or $170. This part # is also in the Husky database, but with a retail price of $257. (so it's worth finding a Jonsered dealer)
At $170, it is probably worth doing, especially if you can do it yourself. At $257??? Be sure to pressure test the saw for air leaks! We are seeing a lot of fuel line failures, so put a new one in as well. The 630's were great saws by the way. If it works out, you'll enjoy using it.