No, the data & power connectors are all standardized. If you connect it to the 4-pin Molex connector, it will be OK whether you're plugging into a 10-year-old machine or a brand-new machine.
The only risk from frying it is if your PSU has issues. That would only be a problem if a) it's so old that it's wearing out & shorting out (which, to be frank, you would notice a host of other issues with the PC before you connected the old HDD), or b) it was of really low quality (again, you'd be seeing problems with other parts first, like BSODs, etc.).