it's lunch time 

would you think it appropriate?

I would.

the girls on reception at our doctor's office eat their morning tea / lunch at the front desk sometimes - I guess they have no choice?

I mean, I would find it inappropriate.

I'd wonder if they weren't able to take a break away from the reception area .

I'd think I'd rather that  than finding no one in the reception area .

How casual were they Icy ? Feet on desks or anything like that ?

Are these staff alloted a proper lunch/break time? Do they have a staff room to sit in to when they have a break?

Why are all 3 having a break at the same time? Shouldn't they take different break times so one is in reception at all times?

would you think it appropriate?

No. I've been in a position where I had to relieve the receptionist so she could take her break and it would have been totally inappropriate or even not allowed to have food on the "front desk"

My own desk,  entirely different story :^O