One of mine dried up completely 2 weeks after kidding(Was abnormal and I pulled kids, but still was milking her 4 times a day) and i have one now that i have been drying up for about 5 weeks. I am still milking her once every night (she only has 5oz of milk but holy heck it is like heavy cream! Very tasty!) I expect she will be completely dried up in the next 1 or 2 weeks.
Boers can take from 2 to 4 weeks or longer, depending on the doe and feed involved.
I feed oat or rye hay and no grain, pull them from the green pasture, if you have that.
I do milk my does every 4 days to check on them and make sure they are not beginning mastitis.
I don't like the idea of just letting them go.
If they dry up with mastitis in there, they will have it when freshening, which will be horrible when the babies arrive.