Answer
Praise be to Allaah.
Yes, that is OK.
It is permissible for the imaam to call the adhaan, say the iqaamah and lead the people in prayer at the same time, because all of these acts are acts of worship and obedience. There is nothing wrong with that, because it is done for the sake of obeying Allaah and drawing closer to Him. And Allaah knows best.
Source: Fataawa Samaahat al-Shaykh ‘Abd-Allaah ibn Humayd, p. 87
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