You might want to read
this thread for an explanation about how to determine if a reboot is required or not.
Anyways, i agree with porter and rhfrommn: regardless of if a reboot being required or not, regardless of the application being affected or not it is better not to take any possible risk and bring the applications down first and reboot afterwards.
Two reasons for doing so even if it is not absolutely required: you eliminated one
possible source of trouble and successful systems administration is often exactly that: stay clear of dark waters even if you know you could swim if you must.
Second: by setting the rules for doing maintenance work
thoroughly you keep the users from becoming "version junkies". If it is no effort at all and can be done without even stopping the application chances are you are asked to apply each and every fix they ever have heard of at the moment they leave the development labs (if not even earlier) - why not? It's only
your effort, not theirs. Usually such an upgrade policy is affecting the systems stability adversely.
If it is
their effort too, because the machine is unavailable for some time and they have to plan for that you usually are asked to keep the upgrade work to the absolute necessary minimum - which is in most cases a good idea.
bakunin