It would work, but Clickhouse is a Russian (Yandex) thing, and SQL isn't really needed for most monitoring and alerting use cases.

If I didn't want to use MySQL or Postgres, I'd rank Prometheus #1 and Clickhouse #2.

The killer thing for Clickhouse is that Percona supports it, so if you want to outsource the installation, mgmt. and support, you can just write a check and get good results.

Also, Clickhouse is a column store with SQL, so you could use an instance for monitoring and another to replace Vertica or Greenplum or whatever so long as it has the client libraries you need.