It depends on what references are broken. By default a project template is for a single project and therefore any binary/project references won't work as you are dropping the generated project into a new solution that wouldn't have the other projects (or likely the correctly pathed binaries). However assembly references to framework assemblies and nuget packages should be fine as they will get properly restored.
If you need to support project references then you'll need to create a multi-project template that can create multiple projects. This is non-standard and I'm not sure it is fully supported but it is documented somewhere how to do it.