Yes, you can implement a binary search for the array container, and yes, during the search it would result in a logarithmic complexity. What I am worried about, is that the complexity is actually hidden one step before. You need to have always a sorted array of elements ready. Each element needs to find its right spot, which will result in far higher complexity than adding an element to a regular map.
As a workaround, TArray may be used only for replication purposes and standalone TMap for computation, but then you get twice the memory size and twice the complexity of adding/removal of items in order to maintain both containers. Seems interesting anyway