Let’s say there is a person who came after the Torah reading has started - I maintain that such person can not be asked to say half-Kaddish after Torah reading. I also read a more strict opinion that a person who did not say Smoneh Esreh can not be called to read half-Kaddish after Torah reading. The same Rabbi maintains that if a mourner is present than it is customary to call a mourner to read half-Kaddish after Torah reading if he said Shmoneh Esreh or at least was present during the whole Torah reading.

Only a person who has heard even a bit of the Kriya can recite the Kaddish prayer that follows the reading. The one who says the Kaddish need not have said Shmone esreh. Kol Tuv Rabbi Ro'I Margalit