Can this circuit drive directly a led ( or even supply a BJT )
As you mentioned, you can directly drive a BJT if you wanted a high brightness LED.

However if you want to connect and LED directly in series with the output this won't be an issue as long as you select the correct LED. For example take this LED (I typed Red LED in Farnell and just grabbed the first one), now what you need to look at is not the tables but the graphs.
If you take the value from the table it says you're looking at a 2V to 2.5V drop across your LED, however this is only true at 20mA. You're going to be operating it at 1/10th of this current.

So let's take a look at the graphs. 

At the 1mA to 2mA range we're looking at a 1.6V to 1.7V drop across the LED (much less than our 2V to 2.5V from the tables). If we take the voltage drop at 1.7V then that gives us a current of 1.6mA.
Now that we have a current value let's jump across to the second graph, we can see that at 1.6mA we're going to get roughly 25% of the luminous intensity than if we were running at 10mA.
From the table it says that at 10mA the luminous intensity (lv) is typically 50mcd. So if we use this LED in your setup the equivalent lv is going to be ~12.5mcd. I know that mcd isn't really a good measure of brightness but I don't know the equation to change it into lumens, I can however, say that it will more than likely be clearly visible.

As a side note, whilst this is all good in theory, it would be much quicker to follow FakeMoustache's initial advice of try it and see.