I would say no.
For example, you'll save some product or whatever in the database, and show a success page or redirect, thinking everything has been saved. But the transaction won't be committed yet and could still rollback after you have displayed the success message.
And with Hibernate, the probability of this happening is even bigger, because nothing will be written to the database until flush time, which will happen just before the commit.
Moreover the transaction will live longer than necessary, preventing other transactions to procees in case it has put a lock on rows or tables in the database, resulting in poorer performance and scalability.
What's wrong with the default Spring OpenSessionInViewFilter, which lets the session open, but still uses service-level, short transactions? Why do your requests open multiple transactions? My quess is that you're doing too many calls from the UI layer to the service layer in a single request.