The antioestrogenic effect of pomegranate
No, supplements containing pomegranate extract can't replace substances such as tamoxifen or anastrozole. But they probably can reduce the conversion of testosterone into estradiol, according to this American in-vitro study at least.
Pomegranates – the fruit of Punica granatum – contain relatively large amounts of polyphenols, of which the ellagitannins are the most important. Micro-organisms in the intestines convert these into urolithin A and B, and these compounds are absorbed by the body. [J Agric Food Chem 2006;54(23):8956-61.] Research on breast-cancer cells has shown that these reduce the effect of estradiol and inhibit the growth of prostate and breast cancer cells.

In the body urolithin A and B are metabolised further to form methylated urolithin A (MUA), dimethylated urolithin A (DMUA), acetylated methylated urolithin A (AMUA), methylated urolithin B (MUB), acetylated urolithin B (AUB) and urolithin B sulfate (UBS).
Aromatase inhibitors

In 2010 oncologists at the University of California in Los Angeles measured the antioestrogenic effect of all these substances in in-vitro studies. They looked at whether the substances inhibited the enzyme aromatase. Aromatase converts testosterone and androstenedione into female sex hormones.

And lo and behold, a number of the metabolites turned out to be aromatase inhibitors: methylated urolithin B performed particularly well.
In experiments with MCF-7 breast cancer cells, urolithin B inhibited the effect of aromatase.

The figure above is taken from an experiment in which the researchers exposed MCF-7 breast cancer cells to testosterone. Because the cells used synthesise aromatase they are able to grow, but as you can see urolithin B in particular impeded this process.
"The ingestion of pomegranate juice can lead to concentrations of circulating urolithins reaching up to 18 microM in blood", the researchers write. "Taken together with the results of current studies and reports of the presence of UA and UB in the blood and urine of human subjects following pomegranate ingestion, the results of these analyses suggest that pomegranate intake may be a viable strategy for the chemoprevention of breast cancer."

Maybe pomegranate supplementation might be useful for athletes too, even though pomegranate supplements are not a replacement for medicines such as anastrazole or tamoxifen. "Six of the ellagitannin-derived compounds, MUB, UBS, UB, AUB, UA and MUA exhibited significant anti-aromatase activity as measured in the microsome assay", the researchers write.
"However, this activity did not reach that of known aromatase inhibitor drugs previously tested in our laboratory."
Cancer Prev Res (Phila). 2010 Jan;3(1):108-13.