Yeah, technically it's producing "some" output at 8 Hz, but the integrator is just EQ'ing the thing. Pretty much trying to squeeze blood out of a turnip - you aren't going to get anything useful down there. It's a 60Hz closed box (as is a fridge cabinet). In a small room, it might be useful. Might.
Yes that is the way it's designed to work.
The general theory is sealed cab rolls of at a rate of 12dB per octave below resonance. AFAIK Bag End INFRA cabs are generally tuned to roll off from about 80hz. The Bag End Dual Integrator applies a 12dB per octave rising response to mirror the natural roll off. The integrator also has some built in tricks to include limiting to prevent over excursion and Concealment which shifts the LF cutoff higher as the system approaches its LF limit.
Here's discussion on Concealment:
To get strong output at the lowest frequencies you need a lot of cabs and a lot of power. The general rule is doubling the cabs and doubling the power gets you 6dB more output. As the specs show, the D12E is rated 123dB at 80hz and 88dB at 8hz; so output at 8hz is 35dB lower than output at 80hz. If I am doing the math right

, you would need at least 57 D12Es for 123dB at 8hz. Since each cab is rated 400W that means you need 57 x 400 = 22.8kW. Also since each cab is 69lbs it means the subs weigh 3,933lbs...let's call it two tons

. Probably not doable for most of us.
What's Reasonable With D12Es? Of course that's on each person to decide for themself. For the D12E, output at 40hz is 11dB down from 80hz. To get 123dB at 40hz requires about 4 D12Es. For 123dB at 20hz you need about 15 D12Es.
Real World Experience:
I built a system using 4 of the S18 Compact subs pushed with 400W per cab. The S18 Compacts had 1/2 the internal volume of the regular S18, which AFAIK incurred a bit of a penalty in sensitivity.
IME a single quality 18" sub would easily bury four S18 Compacts in regards to SPL. However the four little subs worked well for a cover band that played at moderate volume.
The LF cutoff was adjustable on the old ELF 1 integrator I used. I experimented and chose to cut the S18 Compacts off at 40hz. Letting them run lower than 40hz resulted in the Concealment circuit producing fairly audible artifacts well before the mains ran out of headroom. With the type of material we played, the 40hz cutoff worked well.