Be careful with it, since the pressure level from the ATX pump may not be as high as what it'd see with coolant or oil going through it.
I used the external ATX cooler with my MTX and an electric pump for a long time, but I've since deleted it.
If you want to cool the oil a bit better, there are adapters and purpose-built oil coolers that'll do that for you. There are a number of examples (probably in threads here) of doing that at the oil filter adapter like you're describing. Mine is set up that way.
If you used the ATX cooler to cool the coolant further, I'd be worried about leaks as well as perhaps making it harder for the t-stat to regulate the temperature, depending on how that portion of the system is plumbed (it might not matter).
I see more downsides than upsides, basically.