I have an application that requires Google Chrome to work. So I check if Chrome is installed using canOpenURL with URL scheme of Chrome. If it's not installed, tell user it's required to install.
So is this a reason to reject for Apple submission? When download the app, use the URL scheme to access the Apple store so I don't download any binary, I request this action to OS.
Apple won't reject if you app asks to download another app.
If you want the other app required to be installed, you can find a custom workaround.
One example is to show an alert unless that app is installed. If user comes back to your app without downloading the other app, you'll show an alert again.