I've realized (by reading the manual, embarrassingly) that "Transaction synchronization" is about binding resources to the current thread, and is optional. So the answer is yes, you can have resources such as a JDBC connection be released straight-away by configuring the transaction manager to never use transaction synchronization e.g.
Code:
<bean id="transactionManager" class="org.springframework.transaction.jta.JtaTransactionManager">
<property name="transactionSynchronization" value="2" />
</bean>