In your case NO.
The EJB 3.1 spec section 13.6.1 says this for BMT:
The container must manage client invocations to an enterprise bean instance with bean-managed transaction demarcation as follows.
When a client invokes a business method via one of the enterprise bean’s client views, the container suspends any transaction that may be associated with the client request...
This will be similar in earlier versions of the spec.
If you want to have such behavior use TransactionManagementType.CONTAINER, here it will be possible.