The default Paas installation packages will have Application insights enabled by default, so you should not have to configure anything further in Visual Studio for them to send telemetry to App Insights.
However, by default Sitecore 9 does not collect the dependency telemetry, and hence the Application map is unavailable. This is to "optimize resource consumption" as outlined in the kb link below.
However, you can enable the dependency telemetry by modifying ApplicationInsights.config in your solution. Details from the following KB article:
To enable the collection of "dependency" telemetry events, uncomment the following line in the ApplicationInsights.config file located inside the website root folder:
<!-- <Add Type="Microsoft.ApplicationInsights.DependencyCollector.DependencyTrackingTelemetryModule, Microsoft.AI.DependencyCollector"/> -->
Keep in mind that on a busy site this will collect a lot of data, so keep an eye on your App Insights service quotas. You can set caps and warnings in Azure portal if neccessary. Additionally you may see a performance hit enabling the dependency telemetry (as alluded to in the KB), so test and provision appropriately to make sure you're not introducing too much overhead.