It's not the job of philosophers or scientists to check whether Christianity or any other religion is testable; it is the job of Christians to provide a test which is strict according to whatever set of rules the other folks have set up. In this case, if you are asking about scientifically testable, we are talking primarily about a falsifiable statement about religion. So far, none has been brought forward that matches scientific standards. So, no, Christianity is not testable.
The example you gave is something completely different. Your example is basically "belief in something, no matter whether wrong or false, can lead to improved mental health". This statement has nothing whatsoever to do with religion, but is a purely natural statement about the human brain. It is easily testable, indeed we are doing it often. You can search for "placebo" on PubMed and will find plenty of meta studies which prove beyond doubt that this effect exists for all manners of effects.
For other religions the same applies - for example if you look at Buddhism; a fresh convert to that religion may take up meditation practice for the first time in their life, and it is very likely that they get a positive result from that alone (completely irrespective of whether the more religious tenets of Buddhism are "true" in any scientific sense).
Some religions are very intense on certain practices to be held up by their believers; i.e. the commandments of Christianity, or the "path" of buddhism. It is pretty clear that these behavioural patterns alone (i.e. "doing good" for a lack of better description, or at the very least avoiding evil deeds), no matter whether any of the spiritual propositions of the religion are true or not, can have a measurable positive impact on their live, or at least get rid of some less benefitial effects. I.e., if you lead a "gangster" or "drug dealer" life, you will very likely live in more dire circumstances than someone swearing off of that (and being able to exit those circumstances...). The significantly less stress you have in your lifeReal-world aspects like not being shot to death by abandonding those might as well have huge health benefitsother gangsters or the police aside, the significant stress reduction alone might as well have huge health benefits.
N.B.: all of the above is available to any human without any religion or belief system at all; and religions can and have of course also contain content which can be quite detrimental.
TLDR: no, there have been no falsifiable tests brought forward to "prove" Christianity (whatever that may mean, even) or any other religion. Yes, there are testable and readily verifiably experiments which would show that some of the the more practical guidelines of how to behave, contained in many religions, may have beneficial results - irrespective of the religious content - and which can clearly explain people turning from miserable to "glowing", like in your example.