Can a CD74HCT4094E shift register output 20mA?
No, it just means that you can load the protection diodes at the outputs with max. 20mA without damaging the chip permanently.  

This may happen if you apply e.g. a voltage &lt; -0.5V or > Vcc + 0.5V at the outputs (no good idea).

"Absolute Maximum Ratings" give only answer to the question about what you can do without damaging the chip. That doesn't mean that it works properly under those condidtions (e.g. that the output voltage level will be in the required range). 

(That is obvious if you lokk e.g. at the DC supply voltage range Vcc=-0.5..7V. Of course the IC doesn't work properly with e.g. Vcc=0.2V; it's just not damaged)

If you want to know what you can do under operating conditions, you have to see the specifications under "operating conditions".
If you can't find the interesting values in the datasheet of the specific IC you will probably find it in a datasheet for the logic family.