É possível autowire um bean com escopo de solicitação em um bean com escopo de aplicativo. ou seja,

Eu tenho uma classe RequestScopedBean:

class RequestScopedBean {
   ....
   ....
   ....
}

e uma classe Beans com escopo de aplicativo no qual o bean com escopo de solicitação é autowired.

class ApplicationScopedBean {
   @Autowire
   private RequestScopedBean requestScopedBean;
   ....
   ....
   ....
}

e o xml spring-config é o seguinte:

<?xml version="1.0" encoding="UTF-8"?>
<beans
    xmlns="http://www.springframework.org/schema/beans"
    xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
    xmlns:util="http://www.springframework.org/schema/util"
    xsi:schemaLocation="
              http://www.springframework.org/schema/beans  http://www.springframework.org/schema/beans/spring-beans-3.0.xsd
    http://www.springframework.org/schema/util  http://www.springframework.org/schema/util/spring-util-3.0.xsd
">
<bean id="applicationScopedBeans" class="ApplicationScopedBean" />
<bean id="requestScopedBean" class="RequestScopedBean" scope="request">  
</bean>
</beans>

Quando tento executar este aplicativo, a criação do bean de applicationScopedBean falha com o seguinte erro:

Caused by: org.springframework.beans.factory.BeanCreationException: Error creating bean with name 'ApplicationScopedBean': Injection of autowired dependencies failed; nested exception is org.springframework.beans.factory.BeanCreationException: Could not       autowire field: private RequestScopedBean requestScopedBean; nested exception is java.lang.IllegalStateException: No Scope registered for scope 'request'
    at org.springframework.beans.factory.annotation.AutowiredAnnotationBeanPostProcessor.postProcessPropertyValues(AutowiredAnnotationBeanPostProcessor.java:288)
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.populateBean(AbstractAutowireCapableBeanFactory.java:1074)
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:517)
    at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:456)
    at org.springframework.beans.factory.support.AbstractBeanFactory.doGetBean(AbstractBeanFactory.java:312)
    at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:192)
    at org.springframework.context.support.AbstractApplicationContext.getBean(AbstractApplicationContext.java:1075)
    at com.amazon.coral.reflect.instantiate.SpringInstantiatorFactory$1.newInstance(SpringInstantiatorFactory.java:168)
    ... 19 more