A compile-time dependency is generally required at runtime. In maven, a compile scoped dependency will be added to the classpath on runtime (e.g. in wars they will be copied to WEB-INF/lib).
It is not, however, strictly required; for instance, we may compile against a certain API, making it a compile-time dependency, but then at runtime include an implementation that also includes the API.
There may be fringe cases where the project requires a certain dependency to compile but then the corresponding code is not actually needed, but these will be rare.
On the other hand, including runtime dependencies that are not needed at compile-time is very common. For instance, if you’re writing a Java EE 6 application, you compile against the Java EE 6 API, but at runtime, any Java EE container can be used; it’s this container that provides the implementation.
Compile-time dependencies can be avoided by using reflection. For instance, a JDBC driver can be loaded with a Class.forName and the actual class loaded be configurable through a configuration file.