Concur, you gain SI due to an effect that is removing the last character from a side of the battle, and if it is the current battle that character can play an enhancement to interrupt or negate the effect.
I feel like some people are confused about SI and Side Battles, and that it stems from the Real Rulings. Is there a question about how SI works with them? In the case indicated, there is nothing special that would preclude SI in that side battle.