Stranger things have happened; but it's unlikely. According to the historical record, Alexander's funeral cortège was hijacked by Ptolemy, who brought it to Alexandria (the Egyptian one). Several Roman emperors are reported to have visited the tomb and its occupant, so we are pretty certain that Alexander was still buried there during the heyday of the Roman Empire.
It's not impossible that a later Roman emperor had the body transferred to Amphipolis (assuming that Amphipolis was indeed intended as Alexander's final resting place), but it seems unlikely. Why would they care? Alexander's Macedonian heritage wouldn't have meant much to the Romans.
Edit: just checking this on Wikipedia. Ptolemy initially brought Alexander's body to Memphis. Only later was it moved to a tomb in Alexandria.
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