One can have a married life without intimacy. But would it be a happy or a life well spent? Not really.
To cite my personal example (that's why anonymous), I had a fairly decent sex life when I first got married. Things went downhill when later when I was transferred abroad for few months. Those few months of separation resulted in some hesitation at first and gradually our sex life went from once a week to once in two weeks and soon it was barely once a month. As a person who really craved for intimacy and some human affection, I kept on initiating, I was rejected almost 9 times out of 10.
Then one fine day I caught my wife having an affair. Couldn't understand why she wanted someone else yet didn't want to be intimate with me. My whole world broke into pieces… shattered right in front of me. I started getting anxiety and panic attacks. After all I won't be able to dissolve the marriage, mainly because we have a loving 8 year old kid who loves us both to bits.
The affect this had on my psyche was so deep that I started drinking alcohol a lot as a coping strategy on all those rejections. Actually my shrink just made me aware of that. Yes am in therapy now. I suffer from low self esteem and alcoholism. Just because my wife didn't want to be intimate. Apart from therapy, I have asked for hypnotherapy as an alternative method to reduce my alcohol intake and improve my self esteem. I have just started this journey of self discovery and I hope someday I might just be married and yet happy without intimacy.