No. To ensure security of both your AI endpoints and of the Training environment, service connections cannot be set up within the Training environment. Creators looking to explore these capabilities should leverage the GenAI Connector within your company’s staging or sandbox environment. 

Related:

Will it require any specific permission to configure GenAI connector in my training workspace?

see answer above about Training environment. For other environments, an administrator will need to install the connector into the environment and configure the service connections. Once the services are set up, any user with workspace edit permissions can add the template to their workspace and make edits and customize as desired.