The 107.57 heading implies that alcohol-related offences might be an issue, but the text doesn't specifically mention alcohol.
§107.57 Offenses involving alcohol or drugs.
(a) A conviction for the violation of any Federal or State statute relating to the growing, processing, manufacture, sale, disposition, possession, transportation, or importation of narcotic drugs, marijuana, or depressant or stimulant drugs or substances is grounds for:
(1) Denial of an application for a remote pilot certificate with a small UAS rating for a period of up to 1 year after the date of final conviction; or
(2) Suspension or revocation of a remote pilot certificate with a small UAS rating.
(b) Committing an act prohibited by §91.17(a) or §91.19(a) of this chapter is grounds for:
(1) Denial of an application for a remote pilot certificate with a small UAS rating for a period of up to 1 year after the date of that act; or
(2) Suspension or revocation of a remote pilot certificate with a small UAS rating.
107.59 indicates the problem with refusual to submit to testing.
§107.59 Refusal to submit to an alcohol test or to furnish test results.
A refusal to submit to a test to indicate the percentage by weight of alcohol in the blood, when requested by a law enforcement officer in accordance with §91.17(c) of this chapter, or a refusal to furnish or authorize the release of the test results requested by the Administrator in accordance with §91.17(c) or (d) of this chapter, is grounds for:
(a) Denial of an application for a remote pilot certificate with a small UAS rating for a period of up to 1 year after the date of that refusal; or
(b) Suspension or revocation of a remote pilot certificate with a small UAS rating.