I think it depends on the model of POD - the Bean, Live, and Pro handle it differently. I have the Live and the manual for that (Rev E, pg 3-14) says:

USB 2.0 – POD X3 Live’s USB 2.0 jack lets you connect directly to a USB 2.0-equipped computer, and take advantage of many computer-powered features:
Line 6 Monkey software makes it easy to install software and get updates. Install • driver software with Line 6 Monkey, and POD X3 provides 8 audio inputs to your computer via USB:
1-2 is the main signal, configured on POD X3’s Outputs page for Digital Outs.
3-4 is Tone 1 separately in stereo.
5-6 is Tone 2 separately in stereo.
7 is the sum of the inputs you’ve chosen for Tone 1.
8 is the sum of the inputs you’ve chosen for Tone 2.

So here the USB signal is affected by the Digital Outs settings on the Outputs page (see manaul pg 6-4):

Digital – sets the signal for the digital output. There are four options:
Match Studio/Direct – Digital outputs the Tone and Pan settings as shown.
Studio/Direct Tone 1 – Digital outputs Tone 1 only, panned center.
Studio/Direct Tone 2 – Digital outputs Tone 2 only, panned center.
Dry Inputs – Digital Left outputs the unprocessed input(s) to Tone 1, and Digital Right outputs the unprocessed input(s) to Tone 2.

I'm not exactly sure how it works on the Bean or Pro - but the manual should describe it on the relevant pages.

By the way, if you're recording the dry signal from the X3 it can be very low level (intended for re-amping in your DAW using hte POD Farm plugin).

Also, I would turn off any monitoring in the DAW just to make sure it's not affecting things.

By the way - you'll never hear any midi processing form the X3 - it's not a general midi interface and it's not a midi sound module. It has very limited midi capabilities (essentially sending/receiving/passing thru program and parameter changes).