I get lots of unpleasant distortion when I crank the attenuator way down, but it goes away at conversation level and above. I think it's mainly due to the speaker being non-linear at very low power levels. This effect could depend greatly on your speakers. I'm using a single 12, if you have a 4x12 you're going to be 12 dB louder when you get your speakers to that sweet spot.
If you want effects after the power amp, you need an attenuator or load box with a line output to feed your effects, and then send the effects output to a second (preferably clean, solid state) power amp to drive the speakers. Or, something like the Bad Cat Unleash, which is essentially a load box and clean amp with a loop to insert effects between. You'll need to use a separate FX unit(s), I don't think there's any way to use blocks in the Pod for this... unless you were willing to forego L6 Link. Then, you could use a preamp model on the Pod, then the FX loop block, run the send into the DT's effect return, then run the line out of the attenuator into the Pod's return, then add your post-amp effects blocks, then send the Pod's output to the clean power amp.
Given how easy it is to hit the POD's DSP limit, it probably would make more sense to use an M9 or something similar for the post-amp effects, though.