Okay I set some stuff up and took measurements.
To some degree this is the best possible scenario as I used a small diameter 3" full range TB driver (good sounding too) and an Aurium Cantus ribbon tweeter.
The full range driver was mounted at the top of the box so the acoustic centers are pretty close. Please note!, that with a larger diameter full range driver, and with more distance between the acoustic centers, the effects that you see can be MUCH worse.
The first one is an individual response of the full range woofer and the tweeter (setting on top). The tweeter has a single 1uF cap on it and a resistor. I picked a 1uF cap as it is a commonly used value for adding these tweeters. A larger cap value lets it play down lower and the cancellation effects go lower in range. A smaller value can have less detriment effects but it can still have a detrimental effect in some areas. The effects in the top two octaves are about the same. There is no getting around these effects. If you don't hear them then you are simply not hearing them, but they are still there.
See woofer and tweeter individual responses.
The TB woofer has good top end extension but really lacks detail levels of a lighter weight diaphragm tweeter. The fact that everything it does is a compromise as it is having to play the short wavelengths and the really long ones at the same time makes matters worse. So I can see someone thinking that adding the tweeter up top might help it out.
Also keep in mind that I was able to move the tweeter around to find the best possible alignment and keep them in phase over a wide of a range as possible using my measurement system. In other words, I can make it as perfect in phase as possible. You must also remember though that just because it is in phase at the crossover point or at any given point does not mean that it will be in phase over a wide range or over the whole spectrum.
Also, just because you have a full range driver and no crossover does not mean that you have no shift in phase. The inductive reactance of the voice coil will cause a shift in phase just like any other small inductor.
So here the two are lined up as good as they can get and as perfect to being in phase as possible.
So from 3kHz on up they are still in what I'd call an "in phase" relationship and of coarse the lower they play the more the phase rotation, and at some point it passes 90 degrees and starts going the other way and decreasing output.
Note also that even with a 1uF cap on the tweeter, it still plays quiet low. Even though it is well down in output, it can still cause some cancellation.
Also, a full range driver with less output in the top octave will not couple as much with the tweeter and will not give you as much gain as this particular 3" full range driver that plays well to 20kHz. However, the cancellation effects will still be the same.
Now here is where it gets interesting and it is the measurements that follow that shows just how fragile this relationship is.
Here is the exact same setup, distance, etc, but the tweeter is moved back only 1 inch.
What a mess....
Now we have a coupling effect at 20kHz and some gain.
At about 18.5kHz we have nearly no gain.
From 9kHz to 17kHz we have an in phase relationship and getting gain.
From 5kHz to 9kHz we are in an out of phase range and getting cancellation.
From about 6.8kHa to about 15kHz we have about a 15db swing in response.
From 2kHz to 5kHz we are now in phase again getting some gain again.
Then finally below 2kHz we are back out of phase and even though the tweeter is well down in output by then, it is still reducing output levels slightly in that range.
Keep in mind that this was a movement of only 1 inch. It can get much worse.
Now in the next graph you can give you an idea of what the in room response might look like as the vertical off axis causes more of a wide band cancellation effect.
The first measurement is on axis with the tweeter moved back up so that they are in phase again over as wide of a range as possible. It is the Red line. Next the mic is moved up 4 inches. That is 4 inches from 1 meter away. See Orange line. Lastly the mic is moved up 4 more inches, See Yellow line.
Now with just a very small movement of the mic we see a total swing of nearly 20bd from about 9.5khz to 15kHz.
Now just image how much worse this would be with a larger diameter driver (much worse).
This is why I recommend facing the tweeter to the rear or facing it up. You still get the same added air, and space to imaging, but without the adverse effects to the on axis response.
Does this make sense now?