First, let's define what an install is. Now Apple has installs and your MMP has installs. In Apple's case installs are actually downloads (when users hit the "Get" button). In MMP's case installs are app first opens (when users open an app for the first time).
Installs in SearchAdsHQ come from your MMP. You just need to configure integration with your MMP correctly, and you will start seeing installs on the dashboard.
So the answer is - no, you don't need to include installs as custom conversions in SearchAdsHQ, unless you need them to be configured like that for a specific reason. We get installs from your MMP once the integration is configured without any additional actions from your side.
Where will you see installs?
On the main report dashboard you will see Installs, Install Rate, and CPI, and you will use these metrics to check trends or compare them to each other on the graphs and charts.
You will be able to include Installs metrics into conditions for your Auto Rules (for example, adding CPI is usually a good idea).