grammaticality - Usage of "as such"

ODO has this example:

as such

[often with negative] in the exact sense of the word:
it is possible to stay overnight here although there is no guest house as such

That is, while there isn't anything which might be called a guest house, you could find digs in someone's spare bedroom.

There is a more colloquial use of the phrase, too:

This jersey is too small. As such, it's useless.

That makes use of the main sense of such:

such determiner, predeterminer, & pronoun

1 of the type previously mentioned:
[as predeterminer]:
I longed to find a kindred spirit, and in him I thought I had found such a person
we were second-class citizens and they treated us as such

That is, “I thought I had found a person who would be a kindred spirit”; “We were second-class citizens and they treated us as second-class citizens.” This is similar to my jersey example: “This jersey is too small. Such a jersey is useless.”

Now, your example “He arrived late. As such, he missed the boat” doesn’t fit those forms. You can’t substitute as such with either “in the exact sense of the word” or repeat the relevant noun phrase, because you don’t have a noun phrase.

Your example, while a common construction which is gaining traction, is incorrect. You need a conjunction like Because of this or even a simple So:

Because of the accident, he arrived at the dock an hour late. So he missed the boat and forfeited his deposit.