Another problem with your theory is that we/Scholars don't know who Theophilus was. So we don't know if he was a believer.Scholars are divided on the issue. It is likely that Luke traveled with Paul to Jerusalem were he met with the Apostles. Whereas Theophilus needed to inquire about what took place. Do you see what I mean?
As far back as Origen
Origen (AD 185-254) was the first to suggest that “Theophilus” might be a symbolic term rather than a proper name that Luke was addressing.
Its likely Theophilus was a person and of High Social standing as others suggest. "Most excellent" Theophilus.
There was a high priest named Theophilus noted in history.
Theophilus was the High Priest in the Second Temple in Jerusalem from 37 to 41 CE according to Josephus's Antiquities of the Jews.