Opening with >> corresponds to an fopen(3) mode of "a". My fopen(3) man page says:

Opening a file in append mode (a as the first character of mode) causes all subsequent write operations to this stream to occur at end-of-file, as if preceded the call:

    fseek(stream,0,SEEK_END);

I suspect that fopen(..., "a") accomplishes this by using the O_APPEND flag of open(2) on modern Linux systems. On such systems, the implied seek & write would a single atomic operation (ignoring NFS).