It CAN save you energy, but only if you are on the game enough to optimally click the Level Up button.
Cause you see, the champs refuse to level up without a complimentary back pack. And if you aren't around your bastion all the time to give them complimentary back pats, it's not super worth the investment.
If you do upgrade, the "best practices" advice is typically to OPEN the new slots but don't upgrade them.
i'll second what quinn said about opening new slots rather than upgrading them.
i'll also say that if you want to do this, stock the sparring pit with the highest level champs you can. not only do higher rank champs gain more xp than lower ones, they also alleviate the level up problem somewhat since they level up less frequently. i tend to keep my slots filled with rank 6 champs that are at least level 45 and need to hit the level up button once a day at most.
Once you start to build up gems, I would also recommend opening the base level for all of the sparring pits. You'd be surprised how much food champions you can generate through that over the course of the week. I usually use it to build level 30 food champions in preparation for fragment/fusion events, whereby I then convert them all to 4 star food.
Also, similar to what Carpe_Piscis said above, I also use the sparring pit to take 6 star champions up their last couple of levels. The amount of exp required to take someone from 55 to 60 is quite large, and the energy or brew investiment can be quite long, so I find it better to throw them in the sparring pit for a couple of days and max them out on that
Edit: I wouldn't upgrade the pits either though
Personally, I'm a huge proponent of upgrading it to full. Over time the value will definitely pay off.
But, as EGDNIT said - the value would pay off much sooner if you could stockpile XP. As-is, it really only pays off if you are active enough to check regularly.
If you aren't, I'd suggest using brews to bring your 4* food to level 25 or so, since that way you only need to check once every few hours.
Great advice everyone. I am around during the day so I can upgrade 1-1 or 2-1 for food. I can put higher level champs in over night. I like to build 3-30 and 4-40 that I can upgrade for CvC. I will use my next 300 gem monthly award to open a slot.
I need to spend more time farming the dungeons. I have enough champs but need all types of gear.
If I decide to elevate a pit what is the max XP per hour rate?