Technically, it should be possible.
How to enable it
You could use the constructor EnvironmentVariableSubstitutor​(boolean strict, boolean substitutionInVariables) with the second argument as true to enable substitution inside variables.
For bootsrapping your app with this special EnvironmentVariableSubstitutor​ instance, see WarFox's answer in related question Overriding server connector config with env variables with dropwizard.
The SubstitutingSourceProvider to use environment variables inside YAML files is explained here: Can I specify default values for a config.yml on my java application?.
How it works
Dropwizard Configuration uses Apache Commons Text
Responsible for environment variable substitution is the class EnvironmentVariableSubstitutor.
It is implemented by inheritance and uses Apache Commons Text: extends StringSubstitutor.
StringSubstitutor allows recursive resolution
From StringSubstitutor 's JavaDoc:
Using Recursive Variable Replacement
Variable replacement can work recursively by calling setEnableSubstitutionInVariables(boolean) with true. If a variable value contains a variable then that variable will also be replaced. Cyclic replacements are detected and will throw an exception.
You can get the replace result to contain a variable prefix. For example:
"The variable ${${name}} must be used."
If the value of the "name" variable is "x", then only the variable "name" is replaced resulting in:
"The variable ${x} must be used."