[cockroachdb employee]
Short answer: no.
Long answer: at their closest earth and mars are about 54m km apart, at the furthest it's over 400, with an average of around 225m km, so theoretical latency is varies between 4 and 24 minutes.
CockroachDB uses synchronous replication via raft, and that latency would cause problems as would some other setting like our window sizes and their interaction with timeouts.