Maybe yes, and maybe no.
The LDS Church at that time was much more diverse than this FLDS cult is. Latter-day Saints were coming from Canada, Britain, Wales and other parts of the U.S., gathering together and moving to Utah. So, the gene pool would have been much wider than the FLDS, which basically started with two families.
On the other hand, the percentage of LDS that practiced polygamy during the Brigham Young days was quite small. Perhaps only 10% of LDS men ever entered into polygamous marriages. That may have kept the polygamous gene pool a bit smaller—with only certain families engaging in plural marriages.
[And in the interest of full disclosure, yes, I am LDS. And yes, I am very glad we stopped doing the polygamy thing 120 years ago. One wife is more than enough for me.]
So is one mother-in-law.
My best friend back in high school was/is LDS and he mentioned to me that the polygamy wasn't as common with the rank and file back then, but it got attention due to the high profile types, like Brigham Young.
Now, maybe you'll correct me on this, but I was of the understanding that it was during B. Young's tenure as LDS President that polygamy was given the "go ahead" and not Joseph Smith.