The chazzan is at the end of Avos (first bracha of Shmoneh Esrei) and he says, "...מגן אברם" (without the hei) instead of "...מגן אברהם," (with a hei). Would he be יוצא?
תני בר קפרא כל הקורא לאברהם אברם עובר בעשה
Bar Kaparah says someone who calls Avraham Avram "passes over" a positive commandment
I infer, then, that this is problematic. Since the Gemarrah uses a "long" expression "Passes over a positive commandment" rather than stating "he sinned", it seems to mean that the person missed an opportunity to do a positive commandment, but it is not a sin, per se.
The best option, would probably be to speak to the Shat"z after davening and explain that he should correct the error next time.