Is it possible to capture the
Email-to-Case and create some outbound email using
Message.SingleEmailMessage? Instead of using
Email Services I have to use
The answer is yes, as emails that come into Email-to-Case are captured in the EmailMessage object and can be tagged into with Process Builder. Depending on your needs, you could write an invokable method or flow plugin that could accept inbound parameters pulled from the Email Message and do whatever you want.
So in your example, you could create a process that fires on Email Message and pass some stuff to an Autolaunched Flow that sent an email, or write a class with an Invokable Method that sends a SingleEmailMessage or does whatever else you want with the data from the Email Message.