It is not correct.

In the cited post, '먹다' means "to eat food or drink", but '마음' is not food/drink. '잡수시다' and '드시다' can't be honorific expressions of "먹다" if the object is not food/drink. Instead, '먹다' can be used as "to have thoughts or emotions", so '먹으시다' is the right way to represent honor.

> 그분은 이제야 위기를 극복하려는 마음을 먹으셨다.

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See also:

1. [먹다 in Naver Dictionary](http://krdic.naver.com/detail.nhn?docid=13180000)
2. [Tweet from 국립국어원](https://twitter.com/urimal365/status/435957399581519872)