Are async console applications supported in .NET Core?

Yes, the async Main functions are supported since .NET Core 2.0.

dotnet --info
.NET Command Line Tools (2.0.0)

Product Information:
 Version:            2.0.0
 Commit SHA-1 hash:  cdcd1928c9

Runtime Environment:
 OS Name:     ubuntu
 OS Version:  16.04
 OS Platform: Linux
 RID:         ubuntu.16.04-x64
 Base Path:   /usr/share/dotnet/sdk/2.0.0/

Microsoft .NET Core Shared Framework Host

  Version  : 2.0.0
  Build    : e8b8861ac7faf042c87a5c2f9f2d04c98b69f28d

The support for the async Main functions is introduced in C# version 7.1. However, this functionality is not available out of the box. To make use of this feature you need explicitly specify the C# version 7.1 in your .csproj file, either by including

<LangVersion>latest</LangVersion>

or by

<LangVersion>7.1</LangVersion>

For example for the ASP.NET core 2.0 project:

<Project Sdk="Microsoft.NET.Sdk.Web">
  <PropertyGroup>
    <TargetFramework>netcoreapp2.0</TargetFramework>
    <LangVersion>latest</LangVersion>
  </PropertyGroup>
  <ItemGroup>
    <PackageReference Include="Microsoft.AspNetCore.All" Version="2.0.0" />
  </ItemGroup>
  <ItemGroup>
    <DotNetCliToolReference Include="Microsoft.VisualStudio.Web.CodeGeneration.Tools" Version="2.0.0" />
    <DotNetCliToolReference Include="Microsoft.EntityFrameworkCore.Tools.DotNet" Version="2.0.0" />
    <DotNetCliToolReference Include="Microsoft.DotNet.Watcher.Tools" Version="2.0.0" />
  </ItemGroup>
</Project>

where the Main function can be rewritten as following:

using System.Threading.Tasks;

...
public static async Task Main(string[] args)
{
   await BuildWebHost(args).RunAsync();
}
...

References:

1. C# 7 Series, Part 2: Async Main
2. Champion “Async Main” (C# 7.1)