As BB said, the "Pull Deep" affects the frequency response of one of the tube stages in the preamp. For the IIC+, it affects the response of the tube stage that is right after the effects loop before the signal heads off to the GEQ and the power amp.
Here's the change in frequency response of this last tube stage with and without the Pull Deep...
http://www.flickr.com/photos/50442673@N03/4629417552/
So, it's interesting to note that, when "Pull Deep" is
not engaged (ie, the knob is pushed) that last gain stage actually boosts the treble frequencies more than the bass frequencies. Then, when you engage the "pull deep", the low frequency response of the stage is restored, which makes it feel like the bass has been boosted. But really, the "Pull Deep" simply restores the naturally flat response of that gain stage.
It's also important to note that the boost by the "Pull Deep" isn't actually that large. To recreate the "Pull Deep" you only need to boost the low frequencies about 5.5 dB. Your graphic eq pedal might do +/- 15 dB. Therefore, you don't need to go rail-to-rail with your EQ pedal to simulate "Pull Deep"...unless you really dig the sound!
Chip