The number of errors sent per request makes the impact. It is not expected to sent multiple errors per request to Sentry, most of the requests shouldn’t sent any so if the case is that Sentry becomes unavailable the timeouts (which have been re-adjusted couple of times in the past months) should prevent any major slowdowns but when Sentry is reporting multiple errors per request this can stack up quickly.
However if you want to be sure you can use Relay to solve that problem completely since Relay will accept events even if Sentry is not available and wait for Sentry to become available to sent events so as long as Relay is online your application can send it’s errors quickly.