This depends on the kind of system but is also hard to answer with scientific facts.
While for regular apps, it would make sense to update them before loading it completely. (Like games do.)
For web-apps, this makes sense, out of a technical point of view. Of course it is always better to update the app before fully launching, but sometimes, especially at webservices, it is hard to force everyone out of the app, so sending them such a notification can be the only way to make them update.
Sadly such new solutions are hardly researched or atleast researches are rarely publicised for anyone so making data based answers are hard to do. Especially since it always depends on the target group and variety of users everyone has.