Fixing this problem was as simple as adding start and shutdown goals to jboss-as-maven-plugin executions before and after other configuration:
<execution>
<id>start-server</id>
<phase>process-test-classes</phase>
<goals>
<goal>start</goal>
</goals>
</execution>
<!-- copying driver and datasource here -->
<execution>
<id>shutdown-server</id>
<phase>process-test-classes</phase>
<goals>
<goal>shutdown</goal>
</goals>
</execution>
Also this start goal downloads it's own JBoss instance if one is not provided. So this part is not needed any more:
<plugin>
<artifactId>maven-dependency-plugin</artifactId>
<!-- skipped -->
</plugin>