Is it possible to create a template with no template parameters
No. And you don't need for such workaround because...
to enable the class to be defined in a header file without violating the One Definition Rule
You can define a class in a header file without violating the One Definition Rule.
You can even define the member functions of a class in a header - which I think is the point of this question. Simply declare them all inline. If you define the member functions within the class definition, then they're implicitly inline.
There may be more than one definition of an inline function in the program as long as each definition appears in a different translation unit. For example, an inline function may be defined in a header file that is #include'd in multiple source files.