No you can't!
Consider a simple example. You do a 100 mile work trip for which you are reimbursed at 45p a mile. You do this twice - once in a car A that does 25mpg and once in a car B that does 45mpg.
In your view, you'd ignore fuel because you are 'reimbursed'. Therefore in calculating car ownership costs, both cars would have zero for fuel. But this is simplistic and wrong - for a start, the mileage reimbursment is not for fuel alone it is for all of the costs associated with making that journey - contributions towards depreciation, wear and tear, tyres and of course fuel.
So, back to the two cars. In both cases, you receive £45 from the mileage claim. But Car B used considerably less fuel and therefore means much more of that £45 went into offsetting the ownership costs of your car. Or to put it another way, the more fuel efficient the car, the more money in your pocket!
This is why TCO is such an important and useful figure. It considers ALL of this. You add up all the fuel, tyres, depreciation, insurance, tax and add in your reimbursements from mileage claims and the figure that comes out at the end is how much you ACTUALLY SPENT on running your car. Anything less is misleading.
The only time you can truly ignore fuel is when you don't actually pay for it at all - ie, you have a physical fuel card provided by your employer. Then you can ignore it - provided you add in the tax you pay on the fuel card, which varies depending on the car.