I think it really depends on if you're talking about a completely consumer/snapshot sharing service that is free. If so, I would say "no". Facebook and Flickr dominate and (to my knowledge) neither make money solely on their photo services. (Facebook's only revenue is ads and I doubt Flickr's Pro account covers the cost of the entire service).

If you're talking about a premium/freemium service that is targeted at pro-sumers, then maybe. SmugMug and others (myself included) have shown that it can be done profitably. It's just that with a paid service, you reduce your market considerably (no one wants to pay to upload their halloween party pictures).

But I think there are new markets to explore for paid services. Just depends on who you're trying to reach.