I don't think 'desperation to be with them' is necessarily the healthiest indication of longevity in a relationship.
I got along amazingly well with my boyfriend, we spent most of our time together. It was fun and comfortable, our personalities and outlooks fitted very well. I was happy with everything else in my life too, I didn't feel like I needed him to be happy. If he had left me at the beginning of the relationship, it would have been upsetting/uncomfortable for a while because I thought we were a good match, I'd wonder in the future what could have been - but I don't think it would have been completely devastating. Clearly I definitely liked him and wanted to be with him, for all the right reasons; I don't think I am the kind of person who is even capable of instant intense infatuation though. My feelings have grown increasingly strong over time as we've learned more about each other and grown closer, so now a year later I feel inextricably linked to him. I don't know what the future holds, but so far the relationship has been very healthy and happy with no problems.
I think it makes sense that your feelings grow and things become more certain as you spend more time with them. However, I suppose there is also the possibility that people who aren't really a good match just grow stronger feelings of connection over time purely because of familiarity and shared experience. I think you can feel the difference between a genuinely good relationship and a weak one, but no one's truly an expert in these matters. *shrugs*