No, trademark registration is, simply put, a process of applying for legal protection in given classes, and by listing more classes, your application will not be considered more solid. Conversely, if you apply in only one class, your application won't be viewed as weaker. The examiner will only assess whether you qualify for registration in each of the classes listed on the application.
Theoretically speaking, listing more classes, even if they are all relevant to your business, may actually harm your chances of successful registration. The more classes you choose, the more potential overlap you can have with other already registered trademarks, who can then exercise their rights and oppose your application.
However, the existence of such competition and the strength of their claim varies from case to case, which is why we always recommend entrepreneurs start with a lawyer's check to learn about similar trademarks registered in their intended classes. In Trama, we offer a lawyer's check free of charge and with results within 24 hours.