It is difficult, but not impossible, to use the records of the General Register Office to trace descendants, rather than forebears, of a particular family. The birth indexes after 1900 record the mother's maiden name, as well as the name and surname of the child, so that it is possible to trace all the births of a particular family from that date forward.
Uncovering the subsequent marriages of those children without knowing the names of their spouses is a harder propostion, however. To take one example, the likely range of years of marriage for a Michael O'Brien born in 1905 would be 1925 to 1940; there are certainly hundreds of marriages recorded in the indexes under that name.
It is possible to go through all the Michael [O']Brien marriages imaged over that period on IrishGenealogy, picking out all those that show the right father's name, and then investigate births of that marriage, but in most cases, the work involved makes the task impractical. There are, however, other ways of tracking descendants through land, census, voters' and, sometimes, parish records, as well as newspapers.