You've mentioned parenting, so I assume you and your spouse are fairly young...20's or 30's.
I don't have much information at all about your lives. What are your genders, your careers (or not), family support (or not), there just isn't any background info.
So I'll just toss out my general experience. I've been married for 40-ish years. My husband and I have raised two children, a daughter and a son. We had a "normal" marriage/family life (all 4 of us living together as a family, my husband and I in a traditional husband-wife relationship, including a sexual one) for the first 16 or so years of our marriage. Then we began to have major marital problems.
My husband and I stopped being intimate and managed some kind of schedule around parenting. It was miserable for all of us, and so sad. All the sweetness of our little family began melting away. The kids were teens and it was hard on them, having parents who were like ice to each other (because that's what happens when the warmth is gone from a marriage).
After a bit my husband moved away from the children and I to another town. He and I have remained married, but have not lived together for well over a decade. We are friends and live close to each other. We have never been intimate again.
When the intimacy left the marriage so did the heart of it, plain and simple. The playfulness, the tenderness, the affection. I find myself intolerant of him in ways I wouldn't be if only he would do something as sweet as hold me or kiss me on the cheek. I was terrified of divorcing, so never did. But now I live alone and wonder WTH I've done to my life.
So celibacy...I guess a marriage could survive it. Very, very rarely. Certainly more easily an older couple, married a long time, sure. But a couple married only ten years? There sure better be a massive amount of love, fun, romance, tenderness, caring, listening, respect, affection, and loads of other amazing things going on.
I'm thinking out loud.
Honestly? A young couple? Not likely, no. No. I'm sorry.