I am an undergraduate interested in applying for graduate school in a physical sciences program. I have a good relationship with a few of my professors (it's a very small department). I would like to ask if they would be willing to write a letter of recommendation for my application.
There is one professor who I respect greatly and who has told me in the past that he would be willing to write a glowing letter. He has a great academic reputation; he publishes the most out of all the professors in the small department and in (what I have heard) are top journals in his field.
The trouble is that he has a poor non-academic reputation. For instance, a quick Google of his name will yield a page full of news articles regarding his troubles with the law. These are the top results from the search.
Would a poor public reputation like this have a negative impact on the effectiveness of the reference? In theory, I know it shouldn't. Yet I am aware that real life hardly ever works as 'in theory'.
EDIT: the "troubles with the law" involve an impaired driving conviction. For context, this is in North America.