You'd be better off to still use an App Server such as JBoss AS, GlassFish or TomEE that has proper integration with all the parts you'll be using (such as JTA, JPA, perhaps JSF and JMS etc).
Why so care about EJB and POJOs?
EJB 3.1 is also pojo, u can use Local None interface bean directly.
For my experience before, I think if you want to use Seam3 you shoule use JBoss AS to avoid some strange problems on other AS. I think tomcat is not a good choice for Seam3, the core of Seam3 maybe no problem, but I encountered problem when use transaction, security issues on tomcat before.