Anemones will feed on foreign organisms, regardless of previous feedings. This occurance will be reduced by having a clownfish hosting in the anemone, as any fish that wanders too close to the anemone will be shooed away by the clownfish defending it's territory. As far as nutrition is concerned, I will submit an excerpt from Gerald R. Allen and Daphne G. Fautin's book, titled: Anemone Fishes and their Host Sea Anemones.
Chapter 3, Section 1:Nutrition
"Sea anemones that are host to clownfishes, like many tropical actinians and some temperate ones, harbour unicellular algae within the cells of their tentacles and oral disc. A portion of the sugars produced by these plants through photosynthesis are 'leaked' to their host. This may be the anemone's major source of energy. The widely flared oral disc of many host actinians serves not only to accomodate fish, but its large surface area is well adapted for intercepting sunlight. However, actinians, like all coelenterates, capture and digest animal prey with their nematocysts. We have found small fish, sea urchins, and a variety of crustaceans (shrimps and crabs) in the coelenteronof host anemones. They also appear to feed on planktonic items conveyed by the currents. Although the energy they derive from photosynthesis may be sufficient to live, the anemones need sulfur, nitrogen, and other elements in order to grow and reproduce. These animals are not voracious predators: their prey probably consists of animals that bump into them (e.g. a fish fleeing a more active predator) or stumble over them (e.g. a sea urchin, which has no eyes). Therefor, the supply is probably small and irregular. In hundreds of hours we have spent observing them we have never witnessed a host anemone feeding on fishes. A more predictable source of nutrients may be from wastes of their symbiotic fish. This issue deserves to be studied scientifically. Anemones of some species are capable of absorbing nutrients directly from seawater through their thin tissues, and that may be a source of nutrition for these animals as well."
I'll let you deduct what you wish from this article. HTH