That all depends on what you are doing during quarantine.
Medication/ hyposalinity will effect it, and if you do not keep it under at least a plant rated bulb it will also dither away. Best bet as far as long rune simplicity would be just to have a tank JUST for the algae in case your fish need treatment. Unless you know for a fact that the fish you plan to quarantine are NOT ILL...(aka not from a store unless they also quarantine EVERY FISH THEY GET...unlikely since they are a business). I would actually try to email a marine biologist, or facility the pictures of the algae for ID and info. Who knows, maybe you found a freak strain that can cure gambling addiction? My guess is that it is not something aesthetically pleasing (in comparison to corals) and can take over given the right situation.
I guess I should ask...do you want to keep it? IF so, here are some cool things algae can do.
1)oxygenate-any time there are plants, o2 is being created and waste is being consumed by the plant.
2)diversify ecosystem- The algae when grown out can house thousands of different pods and critters. Ever go fishing and pull the weeds off your lure?? YUM!!! Full of bugs!
3)shelters prey-baby fish, larvae, and anything else really can hide in it
do some experiments. See how the algae does when kept moist in open air, maybe this algae could be utilized in an ALGAE TURF SCRUBBER? I love those things, I used one for months before i got a bigger tank.
Everything in the ocean has a reason, and if you can find what this algae is capable of, it could be very beneficial...at the same time it could be a mutated strain caused by accidentally dropping uranium in your tank. lol, so yea
Try this place, im not sure how credited they are, but i just gooogled ask a marine biologist.
MESA - Ask A Marine Biologist