Technically, it should be possible.
You can add code to your build logic to call the given launch configuration. This is an example of how to get and launch a given run configuration:
ILaunchManager launchManager = DebugPlugin.getDefault().getLaunchManager();
ILaunchConfiguration launchConfiguration = launchManager.getLaunchConfiguration("launchConfigName");
ILaunchConfigurationWorkingCopy launchConfigWorkingCopy = launchConfiguration.getWorkingCopy();
launchConfigWorkingCopy.setAttributes(launchAttributes); // launchAttributes is a Map<String,String>
ILaunchConfiguration newLaunchConfig = launchConfigWorkingCopy.doSave();
ILaunch launch = newLaunchConfig.launch(launchMode, new NullProgressMonitor(), true);
The code above is from a project I worked on recently. I allows you to get a particular launch configuration and customize it as you wish. You could add this code in your build method in your builder.
The only drawback is that it requires that the launch configuration exists already. Alternatively, you could "create" one if it does no exist, by putting the .launch file in the .metadata/.plugins/org.eclipse.debug.core/.launches/
folder. This way, the LaunchManager will be able to find it.