Bungfai, it depends on the aircraft equipment, training and regulation.
If HUD with Cat 3 clearance then, yes, but see below.
With a head down FD, first the aircraft system has to be certificated (relatively expensive AFM approval), then crews have to be trained and approved. Even so, the operator might have decided that additional training/currency cost is not justified if there is a good Cat 2 autopilot. Or alternatively that an automatic approached it is judged to be lower risk than manual flight, but this could still leave a manual landing option from an accurate approach.
The range of Cat 2 visibilities can create some the highest safety risks in low visibility operations. The RVRs can change relatively quickly due to the fog formation or dispersal phases, whereas Cat 3 fog usually involves a more stable fog condition. There are also similar risk issues with other low visibility conditions – snow / blowing snow, rain, cloud base, or dust, where additional risks from crosswind might increase the overall risk, particularly if there is need to manoeuvre at/after DH..
Given the choice, an auto approach is safer.
We shouldn’t ask if we can do something – look for confirming evidence, but instead ask ‘should we be doing it’ search for the safest, lowest risk option. Your company may have done that for you.