In general, if a query in mysqld_exporter collector returns an error, the rest of the collector should proceed.
For example, 1 case is described here: https://www.percona.com/forums/questions-discussions/percona-monitoring-and-management/50152-metrics-lr-down
Query in https://github.com/percona/mysqld_exporter/blob/master/collector/info_schema_auto_increment.go can fail, then the whole Metrics-lr is down. If Metrics-lr is down PMM/grafana will not display mysql variables and may not display some dashboards (i.e. Galera cluster).