I see both sides of this issue, but the crux of the matter for me is the difference between a couple *presenting* themselves as "man-and-wife" vs. the *perception* that they are a married couple.
If a couple has held themselves out as married, referred to each other using spousal terms, etc. then a big wedding with all of the trappings after 10 years and 3 kids would be off-putting to me. I would assume, in this case, that they were already married, so having the big ceremony/celebration would just be confusing.
If, on the other hand, it was a couple generally considered married because of their lifestyle, who had never represented themselves as such, I wouldn't blink an eye, children or no. Just because other people considered them married, or even assumed they were, doesn't mean the couple was obligated to feel that way about themselves, or that they forfeit the right to marry publicly. It might be more tasteful to do a small, private ceremony, but that's a taste issue.
So for me, the situation in the OP might raise my eyebrows for a second, but more in good-natured amusement than anything else, since it seems to be common knowledge that this couple is not currently legally married. If I am incorrect and they have represented themselves as married, my opinion changes.