Is it permissible for the preacher to make the call to prayer and then ascend the pulpit and deliver the sermon?

There is no contradiction between the muezzin being the imam, and Muslims have unanimously agreed on its permissibility and desirability. However, it is a Sunnah of Friday prayer for the adhan to be called when the khatib (preacher) sits on the minbar. If the khatib is also the muezzin, he would miss this Sunnah, though the prayer would still be valid. It is preferable for someone other than the khatib to call the adhan. But if no one else is available, then he may call the adhan, then deliver the sermon, and lead the people in prayer.