Yes. Other sites on the same shared hosting can cause your WordPress site to show critical errors that appear intermittently and clear on their own.
Why this happens. On some servers, several sites share one database instance. If a different site has oversized tables, such as runaway logging tables, the host’s scheduled backup can stall every query on the shared instance while it reads through them.
What you can do. Ask your host whether the error windows line up with their backup schedules, and whether other tenants on the same database server have unusually large tables.