How much autonomy does a church have when its evangelist is receiving outside support?
How much congregational autonomy does a young church, without elders and deacons, and its evangelist is supported by an overseas congregation?
It remains autonomous. Your evangelist is supported, I assume in part, by one or more congregations. "For even in Thessalonica you sent aid once and again for my necessities" (Philippians 4:16). That arrangement is made between the evangelist and the supporting congregations. The local congregation is not involved, nor does the supporting congregation dictate what the local congregation does. They can only decide whether to continue supporting your preacher's work.