Will a plecostamus live with no algae in fish tank?

No. What happens in a fish tank is that ammonia is produced from the fish's waste (it is excreted through the gills, and their poo and uneaten food rapidly breaks down into ammonia). Plecos, by the way, are very messy fish. There is no way to prevent this from happening, and ammonia is extremely toxic to fish, even in tiny amounts. So the ammonia needs to be removed. The bacteria that change the ammonia into non toxic substances live in the filter, so without a filtration system the ammonia in the tank will build up and build up, killing the fish very fast. In order to sufficiently dilute the ammonia without a filter, you would have to do huge water changes several times a day, and in the sort of tank (100 gallons) required to support a fish as big as a Plecostomus, this would be logistically impossible.