Installing the Visual Studio 2015 toolkit v140 on a Microsoft hosted Azure Devops Build Pipeline Agent

Question

I attempted to install the v140 toolset using the 2017 installer:
pool:
    vmImage: 'vs2017-win2016'

steps:
- task: PowerShell@2
  displayName: 'Install Visual Studio v140 Toolset'
  inputs:
    targetType: 'inline'
    script: |
      Write-Output "Starting the installation process. This will take some time"
      $installProcess = Start-Process -FilePath $(Build.SourcesDirectory)/External/VisualStudioBuildTools/installer.exe -ArgumentList "--add Microsoft.VisualStudio.Component.VC.140", "--quiet", "--wait", "--norestart" -Wait -PassThru
      Write-Output "Install Completed with code $($process.ExitCode)"

- task: VSBuild@1
  displayName: 'Build Debug [.sln]'
  inputs:
    solution: '$(Build.SourcesDirectory)/LegacySolution.sln'
    vsVersion: '15.0'
    configuration: 'Debug'
    platform: 'x64'

When I run this in Azure DevOps, the install process exits with code 0 (success) after about a minute. However, when it then tries to build the solution it fails with:
##[error]C:\Program Files (x86)\Microsoft Visual Studio\2017\Enterprise\Common7\IDE\VC\VCTargets\Microsoft.Cpp.Platform.targets(67,5): Error MSB8020: The build tools for v140 (Platform Toolset = 'v140') cannot be found. To build using the v140 build tools, please install v140 build tools.  Alternatively, you may upgrade to the current Visual Studio tools by selecting the Project menu or right-click the solution, and then selecting "Retarget solution".

Has anyone tried this before and succeeded?