No, they are not sterile as a whole. Many women who have IVF have gone on to have natural pregnancies. Sterile means no eggs and no sperm, in which case, pregnancy is impossible without the use of donor eggs or sperm, or embryo adoption.
By that definition, I was certainly in error. However, by that definition, most "sterilizations" are not, since tubal ligation, among other procedures, does not stop egg production.
On a related point, it's interesting that proposals to "sterilize" the poor are rarely directed at men, only at women. Fiscally impractical, one would think, since one man can father many more offspring than one woman can deliver. The procedure is also much cheaper.