No, not relative to hiring nobody. A number of costs to employ someone are fixed or otherwise don't relate directly to salary level.
Certain training, HR, accommodation, and orientation costs are relatively fixed, whatever they pay you. If they pay you in certain fringes like lunch expenses, travel, or memberships, then those don't have to fluctuate with salary. Insurance benefits also do not necessarily float with salary (though often employer-provided life insurance pays a multiple of your annual salary).
If the cost of hiring anybody, including HR, interviews, lost time, training, orientation, and so forth, is $H, and the cost of fringe benefits is $F, the cost of regular benefits is fixed at $B, and salary is $S, then your compensation value $C looks something like:
C = H + F + B + S
If they double S, without scaling H, F, or B to match (or otherwise altering your compensation), then no. This is especially true for companies that provide significant fringe benefits or travel costs for you to do your job (e.g. weekly flight costs and hotel stays) or who pay exorbitant rent for the building that includes your office (e.g. prime Manhattan or SF real estate).