That is possible.
The simplest option is to use compile-time weaving. The Eclipse AJDT plugin can compile for you during development. Ant and Maven 2 also supports compiling with AspectJ. Here I have written a response on how to compile with Ant.
It's also possible to load-time weave the aspects into your code. That is a little bit more difficult, since it's different ways to do it on different application containers. Standalone you have to use a JVM argument to enable weaving.
An example:
-javaagent:pathto/aspectjweaver.jar
I have written more about load-time weaving here.
With compile-time weaving I have good experience on standalone clients, IBM Websphere, Jetty, Tomcat and JBoss. The same code works on all platforms and produces the same result. I have no bad experiences with other platforms regarding AspectJ, I just haven't tried them.