If the mother is hermie-prone it will pass those genetics onto offspring. But since the father's genetics also have a "say" here, the offspring may NOT be as hermie-prone as the mother. I don't think this is as simple as just one "hermie" gene, and its going to depend on the genes in question and their interaction. You may see no hermies in the offspring, some yes and some no, or all hermies. It depends, and I think the only way to really know for sure is to grow them out.
Also, not all "hermies" are created equal. Plants that put out full clusters of male pollen sacs along with female flowers are highly undesirable, and IMO those genetics need to be immediately culled. If the mother plant here is putting out male flowers so badly that your first instinct is to kill it, then do so and don't look back.
On the other hand, plants that put out a few "nanas". . .eh. . .lots of lines will do that. So now its a question of how many, when, why and what your personal tolerance is. Personally, I don't care if plants put out a few "nanas", especially late in flowering. I can deal with that. But your needs may be different if you're running a big room or commercial operation. 4 weeks is pretty early to see "nanas". Is there some specific reason why you think this may be happening? (Nute, light, or heat stress?).
As to whether or not you should keep these, as a first rule, you should only be breeding with the absolute best material possible. If you were a true commercial breeder, then you "should" be killing every hermie plant ruthlessly and instantly. Many don't do it, but in general, one should avoid breeding with hermie-prone plants.
So again, assuming the hermies you see are enough to have you concerned (ie not just a rare "nana") and you have access to better genetics, the smartest thing to do is get rid of the questionable beans and move on. Most growers have limited ability to grow anything, and its usually not worth playing around with genetics you have a good reason to believe aren't up to par.
If you really DON'T have access to anything else, or if you really love these genetics so much that you don't mind taking a chance and basically have more growing space than you need, then it might make sense to keep the beans in question and test them out. But these things probably aren't the case.
... saving one sprout and a bagseed vegging plant that just started showing preflowers. The Blue Hash strain had full on, beautiful male flowers, not just a nanner unfortunately. The other plants I had were the children I had crossed trying to get rid of my last hermie strain. 
, all gone. Nothing left but some really valuable experience. And I'm out of pot! Because of the previous hermies, I haven't in a year of growing, been able to get enough to smoke. Forget trying to cure anything...Bottom line, I wanted those genetics gone.