No, it won't. It will be exactly the same as the present setup.
The current battery in the Poseidon is an 18650, sealed into a battery canister that also contains a backup computer and buddy LED light. That battery gives 40-60 hours of dive time from a full charge.
The SSS in a 3rd cell config takes power from the M28 computers that reads it. I get around 25-30 hours off a single charge on the computer, according to the lead diver at Poseidon, the SSS will reduce that runtime but so far he hasn't noticed any significant change (still recharging the computer every couple of days, or before a big dive)
He runs one M28 and SSS, and another M28 to control the CCR, he hasn't seen any significant differences in the battery runtimes between them.
I am getting my SSS and 3rd cell pod in 2 weeks, I will give feedback to those who are interested.
Right now, I expect that the runtime on a Poseidon Seven with dual SSS (which they do not recommend right now for other reasons) and the existing battery config will go from 40-60 hours, down to 30-50 hours. Again, I have never lost a dive due to battery low and I have done 3 day liveaboards with 3 x 1.5hr plus dives a day and ended the trip with well over half the battery life remaining. This with not turning the unit off between dives, except when I have to change scrubber.
If you are using an M28 as controller, it can also power the whole unit should the onboard battery fail, via the digital bus.