What are the repercussions of running a 10k race with a hangover?

Hangover and running. Many problems can occur. Alertness and coordination may be effected so a fall or injury may result. Also a hangover is usually associated with dehydration, and a 10k race can add to this and cause severe problems with dehydration and complications that can be serious and even lethal.
Feeling lousy. There is no evidence that doing anything with a hangover causes any more harm (or good) than doing it without a hangover. There may be more likelihood of muscle cramps, since part of hangover is dehydration and electrolyte imbalances.