Is it possible to hook up a dedicated mic pre to my Schiit Yggdrasil?

No. You  can't run an analogue input into a DAC [Digital to Analogue Converter.

Having said that, there are going to be DACs with pre-amp functions and all kinds of mixes available , so I'm not doing absolute truth here. But generally speaking... you'd run a mic pre-amp into an ADC.

The question here is what are you trying to achieve? Where do you want to hear, process or record the output of that mic? You mention streaming and podcasting, so I assume you need it as a signal inside a PC.

You need an audio interface. Or a USB Mic.

I became a great fan of RME, when I put one of their cards in my PC, about 2003ish, and found hifi sound coming out. The only problem that I have them now is that they are not particularly Linux friendly, and I'm not Windows friendly any longer. Actually, my old card works, but it doesn't sound so hifi now. Not sure how much of that is my standards have changed, and how much is some component on the card has aged.  Frankly, my hearing has got a lot worse, so I suspect the card has become faulty.

You just need to be careful you get the right ins and outs. Buying an expensive pro interface that actually only works with  pro studio protocols and connectors would make for a very bad day.

I do think that RME is a step up the pro quality ladder and I doubt that you could go far wrong with a Babyface --- as long as you double check that you will be able to use it in the way that you want to, connected to the gear that you have or intend to buy.

By the way, if I had plenty of money, and didn't mind using Windows (neither is going to happen) I'd buy a Lynx Halo    .

See Gearslutz if you want to  stimulate the salivary glands over this kind of stuff. Enjoy!
 

So how would you rate the Babyface? Or ...same comments apply?

I'm using an AKG 3000B into a Native Instruments 6 pre/A-D. Hanging by XLR cable from a cabinet/shelf so that it's floating in front of me.