Depends on what type of fluorescent lighting you're asking about. Although I wouldn't recommend it for anyone, I have an RBTA under 2X96 watt PC lighting. It's been under that light for almost 4 years and is very healthy.
Also, T5HO is fluorescent lighting and more than enough to keep many types of anemones healthy and happy.
If you're asking about standard NO(Normal Output) fluorescent lighting, No, it'd soon die.