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I would say yes, if you increase your mileage by no more than one mile per week and concentrate on distance, not speed. It probably won't be the fastest time on the planet but if you're happy just to plod round and enjoy it I don't see why not.
I did that - from 10k (and then not running more than 2 miles for three weeks) to a half with less than seven weeks notice. I got round without walking which was my goal.
Congratulations on your 10k time by the way!
The full, i'm slow i'll be one of those right at the back.