As it is on the lighting circuit the FCU is not required. It will offer no discrimination with the circuit MCB.
It would depend on fuse in the FCU and the type of MCB plus type of fault. Some doors are 12 volt the idea is they can be opened even if there is a power cut, clearly required with integral garages with no personal door.
Even with 1A fuse which is the smallest one can normally get for FCU with a short circuit a B6 MCB will still trip first, however other overload faults likely fuse will blow before trip goes.
With a battery powered unit, be it garage door or stair lift, the power required is very low, some where around 20W and unlikely to exceed 50W, with direct mains powered doors however likely a lot higher, around 200W.
Although direct powered units could draw extra power if for example water in tracks has frozen causing a 1A fuse to rupture both saving lights going out and motor being damaged, with the battery backed type it is unlikely any fault will cause an overload on the mains supply. Maybe a faulty rectifier or battery may cause an overload, but for a fuse to protect it would need to be carefully selected, so a 0.63 amp fuse on the circuit board may offer some protection, but the type of fuse found in a FCU is unlikely to protect from this type of fault.
However although items considered as portable the fuse in the plug is only for the cable, with fixed items the manufacturer can stipulate an external protection device, it is common for boilers to require a 3A fuse in a FCU.
I have never tried a 5 amp fuse with a 6 amp D type MCB, not sure which would open first, but have had the 3A fuse fitted inside a fluorescent lamp rupture before the B6 MCB so even a 3A fuse can help.