Ask HN: Can I use another PSU to power a HDD?

I have 2 PSUs, one is an IDE Molex, the other is SATA connectors. The SATA PSU is tempermental, so I use the molex one as I have all IDE devices.

I need attach a few hard drives from another machine which are SATA and my question is, while the computer is powered from molex, can I also plug my SATA PSU into the hard drive, with a SATA cable to my motherboard, and power it that way? Sorry if it doesn't make much sense, I'm rushing and a bit stressed (kids)