No they don't. They have to work out what the job's worth, then add 13.8%* as one of their additional costs of employing that person. There are other costs to employing people, like workspace, equipment, utility bills, insurance etc. And if, once they've worked out the total cost of the employment, they can't afford it, they need to work out where they want to save money - do they cut the wages and pay below market rate for the job (so probably miss out on better candidates), do they increase the prices to their customers (and so possibly miss out of business), do they try to reduce other costs like stationary? If you work out the amount you want to spend then deduct 13.8%, you're always going to have the calculation wrong, because a) that's not how employer's NI works, and b) you're not considering all the incidental costs of employment.
* that is, 13.8% after deductions, of course