Querying ApplicationInsights

Daniel, you're absolutely correct in the query being fine. Unfortunately, right now alerts do not yet support cross-Application Insights-Log Analytics alerts. It is something that is on their backlog, but without firm ETAs yet. I've let them know of this discussion, and they'll reply if there's any additional information available. 

In this specific case however, the good news is that since you're targeting a single app, Application Insights also supports log-based alerts! Instead of creating this alert targeted at your Log Analytics resource, in the Azure portal open the "Sitecore Production" Application Insights resource, select "Alerts" from the left-hand navigation menu on the AI blade, and under target, select "custom log search". Your query would then look identical, minus using "dependencies" instead of "app(...).dependencies" for your first line.