I suggested putting our battery on its side in our robot because that would be ideal for spacing, but one of our mentors mentioned that it causes the battery’s energy to deplete faster. I saw 987 High Rollers with their battery on its side last year and they are one of the best teams in all of FIRST, so my question is: is this an issue, and if so, how much of an issue is it?
It’s how we do it almost every year. If it does drain faster its not going to be noticeable in a 2.5 minute match.
The battery can be operated in any orientation. Sideways mounting allows you to lower the center of gravity which is a often a benefit to the whole robot.
Nope, not an issue. There are even brackets designed to interface with the top of the battery for side mounting.
Just make sure you charge it standing up.
Why?
These batteries are sealed, there are no vents that would require a charge orientation
Thank you so much guys! That makes life a lot easier for us! 
As I understand it, there is a vent for pressure relief.
There are one-way vents to dispel the hydrogen gas that is a by-product of the charging process.
In theory, you will be able to charge it one or two fewer times over the course of the life of the battery if you only use it standing up. It’s such a minuscule difference you’ll never notice it.
Al’s thoughts from a different thread on the same topic.
While these batteries are sold as Sealed Lead Acid batteries they all contain vents to minimize the possibility of explosion. The plastic slab on the top of the battery that looks to be glued in place is where the vents live. The AGM batteries most of use have the liquid acid contained in absorptive fiber glass mats between the lead plates. This does allow some liquid to be present in each cell in the battery. During charge and discharge some of this liquid is turned into gas that will condense on cool parts of the interior of the cells. If enough of this condensate is present and the battery is charged or discharged in the inverted position, the internal pressure may force some of the liquid through the pressure vent. The batteries are really designed in such a way that vapor and condensate will be reabsorbed by the glass fiber mat during normal use. However, there is no method for users to replenish lost liquid that leaves via the pressure relief ports.
So under normal conditions there should be no real concern as long as you are not charging them while they are warm? Basically don’t abuse them and it shouldn’t matter?
Pretty much don’t charge them or use them mounted exactly upside down.
Charging when warm is another issue. Many smart chargers are confused by the testing parameters during charging when the battery is warm. Let the battery sit disconnected for up to 30 minutes to let temperature fall to ambient, then charge. Charging a warm battery usually results in under charge.