Sure it will. You won't be getting the efficiency you'd normally get from the fan motor in the new furnace but there's not a huge difference in power usage unless your old motor is going bad which it could be.
Your furnace on a new 16 SEER system will just be the air mover in the system. The part where you're saving money from upgrading to a 13 SEER or 16 SEER system is in the compression ratios to do the work you need done. The older systems 12 SEER and below used a higher compression ratio than the newer system that have higher SEER ratings.
They basically do this by putting a smaller compressor matched to larger coils. Where the old system (10 SEER) would have a saturation point for the evaporator that was 35° below indoor temperatures the newer system will be 30° for 13 SEER and about 25° for a 16 SEER system.
The older systems (10 SEER and even greater for any SEER less than that) would have a saturation point for the condenser which is about 30° above outdoor ambient. The newer systems will have a saturation point for the condenser which is about 25° outdoor ambient (13 SEER) and 20° above outdoor ambient (16 SEER).
Let's say it's 75°F inside and 95°F outside.
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10 SEER pressures R-22:
Evap. saturation point - 68.56 psig (gauge pressure)
Condensing saturation point - 278 psig
To find the compression ratio you'd add your atmospheric pressure for your location but for this example we'll use sea level.
68.56 psig + 14.7 psi (atmospheric pressure at sea level) = 83.26 psia (absolute pressure
278 psig + 14.7 psi = 292.7 psia
292.7/83.26 = 1:3.52 compression ration
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16 SEER pressures R-410a:
Evap. saturation point - 144 psig (gauge pressure)
Condensing saturation point - 390 psig
144 psig + 14.7 psi (atmospheric pressure at sea level) = 158.7 psia (absolute pressure
390 psig + 14.7 psi = 404.7 psia
404.7/158.7 = 1:2.55 compression ratio
The R-410a system is obviously using less power to do the same work.
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Anyways, the important thing to remember is that you need your furnace to move the desired volume of air to be able to achieve those SEER ratings. That calculation is 400 cubic feet of air per minute per ton of refrigeration.
Your 4 ton system needs to move 1600 CFM. You might want to ask them to verify that your furnace is doing that presently before you go installing a new HVAC system without a new furnace. As in almost all cases I've seen the previous contractors didn't do any sort of detailed duct calculations to match the heat load calculations. The return vents are usually undersized and the supply vents are usually not the correct size for a balanced system.
For example to get a 400 feet per minute face velocity from a single return grille with 1/3" spacing it would need to be about a 30" x 30" return grille with has an Ak (effective area) of 4.363 sq ft.
You can find that data here:
http://www.hartandcooley.com/enginee...a/pg%20110.pdf
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