Among those Rabbis that I know, if/when they are approached by someone who wasn't raised as a Jew but has a Jewish maternal grandparent, they welcome them with open arms as Jews, albeit Jews who have been estranged from their own religion. I have known this to have occurred on multiple occasions (although I was never personally involved in any).
It may be useful here to distinguish between various forms of "Jewishness". According to halakha, that is, Jewish Law, such a person is completely Jewish in the sense that person is bound by Jewish Law (as opposed to Noahide Law) and if that person is a woman, her children retain that status as well.
However, if someone doesn't identify with the Jewish people, then they can lose some of their "Jewish rights". This includes a share in the afterlife as well as in the good fortune of the Jewish people that is promised to them by the Prophets (Rambam, Hilchos Teshuvah 3:11). This is likewise true of Jews who don't believe in the 'Jewish beliefs' (Rambam's Introduction to Perek Cheilek). There are also several laws in the Torah that differentiate between Jews and non-Jews (such as the fact that shehita, ritual slaughter, can only be done by a Jew), and many of those laws only consider those who personally identify with the Jewish faith to be Jewish. This loss of "Jewish rights" is applicable equally to a person was raised in the most traditional Jewish family and someone is merely Jewish by virtue of having a Jewish maternal grandmother, once (s)he could no longer identifies with the Jewish faith.
But, to re-emphasize, such a person is still considered a Jew regarding his/her own legal status (i.e. that person is considered bound by Jewish Law and, if female, will have Jewish children), so once/if such a person decides to identify as a Jew, that person will be 100% Jewish in every respect, and not require any form of conversion ceremony.