Thanks to the link provided by @Igor Romanov in the above comment, here my solution:
val myApp = play.Project(appName, appVersion, appDependencies).settings(
Keys.javaOptions in (Test) +=
"-javaagent:/Users/myName/.ivy2/cache/org.springframework/spring-instrument/jars/spring-instrument-3.2.2.RELEASE.jar",
// code remaining
This allows to apply load-time weaving for class dealing with Spring's aspectj.
The whole works pretty well :) (tested with SBT 0.12.3, Scala 2.10 and Play 2.1)