I seem to remember some discussion in another thread or two on the forum about saw palmetto and estrogen... but I don't recall exactly was said in the end. Perhaps a search will turn up those discussions.
If you just look at a monograph on it, however, you can see (emphasis mine) that there may well be cause to investigate at least the statement, "It can't hurt" and the idea of running it year-round as a regular supplement.
NOTE: I am not saying you should or shouldn't use saw palmetto or making any comment to that effect, only sharing information.
Saw palmetto ( Serenoa repens, Sabal serrulata ) is used popularly in Europe for symptoms associated with benign prostatic hypertrophy (enlargement of the prostate). Although not considered standard of care in the United States, it is the most popular herbal treatment for this condition.
Multiple mechanisms of action have been proposed, and saw palmetto appears to possess 5-alpha-reductase inhibitory activity (thereby preventing the conversion of testosterone to dihydrotestosterone).
Hormonal/estrogenic effects have also been reported, as well as direct inhibitory effects on androgen receptors and anti-inflammatory properties.
--Natural Standard® Patient Monograph; from MayoClinic.com