This is a hypothetical designed to investigate a subtlety of practice and understanding, not elicit a halachic ruling.
I will be attending a morning shiva minyan on Monday. The mourner is a kohen and will be the only kohen present at the davening. I don't know if in that case he is supposed to get the 1st aliyah, but I have read that "If he is called to the Torah by mistake, he may accept." So in this hypothetical, the gabbai mistakenly calls the mourner, who has the aliyah.
I also know that during a shiva, the tradition is not to open the conversation with the mourner or greet him: "A mourner is forbidden to say hello or goodbye; likewise we do not say hello or goodbye to a mourner. We do not say "shalom," or any other greeting" (cited from Shulchan Aruch, YD 385:1 here).
Generally, though, when someone receives an honor during services, such as an aliyah, it is proper to say Yishar Kochacha (or some variant, depending on tradition/pronunciation).
But is that, as a greeting, inappropriate during a shiva? Is the mourner still sitting shiva while he is participating in the service (on a non-Shabbat/holiday) or are the laws suspended (if he is accidentally called for hagbah, can he sit down with the torah in a regular chair)?