It is quite possible. Heck, you can even add
JSF to an old web application. The functionality you are gaining comes as additional services not as something that will conflict with older stuff.
I have a project, in fact, that was done with a proprietary MVC and ORM service and I've been slowly migrating stuff as enhancement requests came it. The only real issue I have with this legacy code co-existing with my newer Spring/JSF code is that the old ORM's entity classes couldn't simply be annotated into JPA entity classes because the old ORL did some questionable things with its objects (they're not POJOs, for one thing). So I occasionally have to transfer stuff between new and old ORM models. Which isn't a Spring issue. Even if I was using JPA without Spring, the modelling confllcts would still exist.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.