Yes, there are benefits to breastfeeding beyond the milk. Physical - breastfeeding allows normal mouth and jaw development. The act of nursing using muscles in the face and jaw that aren't used in bottlefeeding. It creates that round facial structure, the pudgy cheeks of the breastfed baby, and helps with jaw/tooth alignment (potentially reducing the need for orthodontia later in life).
Any amount of breastmilk reduces the risks involved in artifical feeding. Studies that actually quantify exclusively breastfed vs. partially breastfed vs. artificially fed show a dose response. Those babies who are exclusively breastfed have the best results, but those getting some breastmilk fare better than those fully artificially fed. And far too many of the studies that show risks to not breastfeeding consider *any* breastfeeding in the breastfed group, which is good news for babies getting both breastmilk and artificial baby milks.
But probably the most important is the emotional and bonding benefit. No matter WHAT your DS is drinking at your breast, he's there. He's being held for each and every feed. He's skin-to-skin for every feed (and that has a physical effect as well, releasing hormones in both of you such as oxytocin that lower stress response, lower blood pressure, etc). He's interacting with you for every feed. It's hard to quantify those effects, but they are real and meaningful. As an LLL Leader once said to me, "if my breasts made formula instead of breastmilk, I'd have a real struggle deciding how to feed my child."
If he's getting, say, 10 feeds a day and is getting 2 oz of formula per feed, then you're still providing between 30 and 50% of his milk (most breastfed babies take btwn 30-40 oz of milk in 24 hours). That's definitely a meaningful amount.
I found the SNS to be a pain in the rear. I've heard many moms say that the Lactaid is easier to use and maintain. If it seems that you're going to continue supplementing long-term, you might give it a try. If you haven't already gotten in-person support from an IBCLC who has experience with low milk supply, I'd also encourage that. The book "The Breastfeeding Mother's Guide to Making More Milk," by Diana West IBCLC and Lisa Marasco MA, IBCLC, as well as their website lowmilksupply.org are good resources as well.
Good luck. It IS the worst of both worlds, but if you can find ways to make it easier, you're giving your son a wonderful gift.
