Yes, drawee is a Scrabble word!
...and is worth 10 points in Scrabble, and 10 points in Words with Friends
drawee
Noun
1. The person (or bank) who is expected to pay a check or draft when it is presented for payment
What Scrabble words can I make with the letters in drawee?
5 Letter Words
4 Letter Words
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3 Letter Words
2 Letter Words