Some people even recommend adding a few drops when you add new fish to the tank because it's soothing so I'm sure it's fine to add to the whole tank. Didn't do mine any harm.
Adding medications when there is not a disease to treat is a very poor idea. All you end up doing is selectively breeding medicine-resistant strains of the bacteria in this case. Think about it, you add medicine, it kills off the bacteria that a susceptible to it. Now, the resistant bacteria can grow faster because there is less competition. That susceptible bacteria may have even been keeping the resistant ones in check via competition. Maybe that resistant bacteria that is growing faster causes a problem, such as fin rot. You try to add Melafix, but, it is the resistant strain. And now you have to go to stronger and potentially more dangerous medicines.*
Please just reserve adding medication until you actually have a disease to treat.
Re the biological filter, melaifx is a fairly mild anti-bacterial. A lot of how it works is that it slows the rate at which bacteria grow. For the fish, this gives the fish's own immune system a chance to catch back up, so-to-say. Hopefully, you buy enough time for the immune system to catch up and treat the infection in its own. For the colony, it's growth will be slowed also, but if the tank is cycled, growth is only needed to replace the cycling bacteria that die. Bacteria do die all the time, but it is usually just a tiny % a day (I don't know, but if they are being fed I cannot imagine it is more than 2% a day, and probably like 0.1% a day). Since the melafix is in there, the colony won't be able to replace the dead members as quickly as it would otherwise be able to, but unless you treat with melafix for longer than 2, 3, 4, maybe even 5 or 6 weeks, this resultant shortcoming probably won't even be noticeable. If you have to treat with melafix for that long, you've probably got a bigger problem on your hands anyway, which will necessitate using an anti-bacterial that probably will kill the colony.
* p.s. I wanted to give you a bigger example of the problem of casual medication. Staph infections used to be a minor bacterial infection that people occasionally got when they went into a hospital. It normally required giving the patient penicillin in addition to whatever else the patient needed. Well, eventually a penicillin-resistant strain developed. So, stronger medicines had to be given. And so on and so on. Today, there exist strains of staph that are immune to every anti-bacterial known to man, and the death rate from these super-staph strains are increasing every year. The rate of mutation and adaptation of the bacteria is far greater than the rate of discovery of new antibacterials. Among the biggest culprits? Parents who demand that their children be given antibacterial medications when they get a cold. A cold, caused by a virus! Antibacterials do
nothing against a virus. Yes, in rare cases doctors should give someone with a viral infection antibacterials to prevent secondary infection, but the rare cases are for immunocompromised or otherwise weakened systems. Another big culprit? All the anti-bacterial soaps, and lotions, and cremes, and wipes, and cleaning products, even though regular soap and water kills bacteria just as effectively. There is even evidence that bacteria trade genetic material with each other, so if a common harmless bacteria mutates to become resistant to your anti-bacterial soap, it may pass that information along to a dangerous bacteria species. And again, now when you use that anti-bacterial cleaner, it is resistant, and may grow uncontrollably once you kill its non-immune competition, and become dangerous when otherwise it may never have reared its ugly head. The UK has taken a stance on this, banning many common anti-bacterial household products. I wish the US would wake up and do the same. And I wish that doctors, who know better, wouldn't cave in to pushy parents and patients. The doctor should explain to the patient the dangers of casual antibacterial use. Maybe someday, but the whole point is that casual antibacterial use does more harm in the long run than good it may do in the short run.