I don't think anyone looking to trade for a rental catcher would be interested in giving up pieces that help you win now, whether that's in the bullpen or elsewhere. But the Twins don't necessarily have to get their pen help directly through one trade.
If they traded Jeffers for prospects (it's not impossible that someone out there is willing to give up pen pieces for him, but I gotta believe your market will be bigger and your return more valuable if you accept prospects) and also traded prospects for relief help (doesn't have to be the same prospects you received for Jeffers), they've effectively landed where you'd be if you'd have swapped Jeffers for relief help, only you've had more flexibility to find the right relievers. They could accomplish this in a three-team trade, I suppose, if the third team was supplying the relievers.
I guess my point is I hope they don't shop Jeffers with too narrow a scope regarding the return, since how they net out after all their trades is what really matters