It works great for some people, while others don't get much from it. If you have anxiety issues then it's worth a shot but it's important to understand what you're doing, why you're doing it and how you're going to do it without running into trouble.
What you would be doing isn't treating your anxiety but covering it up. It will only get better when you're actually on the drug with the possiblity of having even worse anxiety on your off days. Phenibut seems to be somewhat unpredictable in this department and experiences with rebound anxiety differs greatly between different people. As in, some don't notice any increase in anxiety after 3 days of use while others only need one dosage to make matters worse the next day.
It also works as a pretty effective anti-depressive drug for some people, myself included but I definately wouldn't go as far as labeling it "good for overall mental health" - healthy foods, exercise, sufficient sleep, meditation, yoga and such are the things that belong in that department, not one drug comes to mind (psychedelics have the potential but it's pretty far from a safe bet like the above mentioned stuff).
If you're going to try it, then I would encourage you to make up some rules for yourself very early on in your Phenibut adventure so that you don't end up regretting it in the future. Keep in mind that those who regret trying it most often do so big time! The withdrawals are insane and it takes only a week or two of use to get physical addicted.
As a frame of reference, this is my own rules.
Max dosage 1500 mg (most of the time 700-1200 is enough)
Never use two days in a row
A maximum of one dosage a week
Take 2-4 weeks off every now and then.
Don't mix with alcohol (some people do so without problems if the dosages are adjusted accordingly )
If combined with benzos or other GABA-A PAM/agonist, dosages should be adjusted accordingly)
Following these rules or something similar should keep you safe from harm. Be aware though, that even with a set of well defined rules, you could still run into trouble. Addiction can happen regardless of the steps you take in order to prevent it.