I would try it and watch your babies cues. I never had to feed on both sides after my boys reached 2 weeks old. I always had so much milk that I was drowning them. So, I never bothered with the second side. The nurses and my Dr. told me, that using the other side (for me at least) would be more if I was getting engorged and needed to gain some relief. Basically, I was told to only nurse on the second side for my comfort. But that was me, and I was still spraying milk across the room after a full feed on only one side.
I think you need to figure out what is best for you and your baby. Unfortunately, you can only know this by trial and error. If you try it and it doesn't work, you still have the other side to fall back on, so I think it would be worth a shot.