What is the impact of starting Microsoft SharePoint Foundation Web Application Service in Application Server?

I have a SharePoint 2013 server farm with 4 SharePoint servers (2 web front end and 2 application servers) + 1 SQL server.

I have a custom SharePoint solution which can be deployed globally. When I deploy this solution using either Central Admin or STSADM.EXE or Powershell, I am seeing that the solution is being in “Deploying” state for some time and then it is changed to “Not Deployed” state.

When I open the solution from Central Administration, it says that solution is successfully deployed to 3 servers and fourth server (one of the application servers) is not listed there and there is no error message.

“Microsoft SharePoint Foundation Web Application” service is not running in both the Application Servers but the solution is being deployed to one of the application servers.

Can I start “Microsoft SharePoint Foundation Web Application” service in both the Application Servers? What is the impact of running this service in application servers?

or is there anything else that I can do without starting this service in application servers?

Thanks in Advance.