In a word, no. All of that water is inside the building, and it doesn't matter how long it takes to heat it all up- BTU/hour is the same as heat/time. If it takes 15 years to heat it all up with a 1BTU/hr candle, it doesn't matter, as long as the house only needs 1BTU/hour.
The only thing that matters regarding the boiler output sizing it the maximum rate of heat loss out of the house- the BTU/hour leaving the house at the coldest hours of the the coldest night of the year. The calculating the heat loss at ACCA 99th percentile outside design temperature (based on 25 year binned hourly weather data during the heating season) for your location is more than sufficient for sizing the boiler to keep you warm. Going a whole lot larger than that results in lower efficiency and lower comfort.
The total amount of BTUs stored in the water at 180F (or any other temperature) is irrelevant. It's the rate at which it can release that heat to the house that counts, and that changes with temperature (and the size of your radiators.) The higher the difference in temp between the water and the room, the greater the BTU/hour rate, and the larger your radiators, the greater the BTU/hour rate at any given temperature. But you only need the water temp at which the heat emitted by the radiation matches the heat loss out of the house, and that heat loss also varies with outdoor temperature (and other factors, such as passive solar gain, wind-washing, etc.) Outdoor temperature is a very crude model for tracking the heat load, but it's "good enough" so that using an "outdoor reset" sensing the outdoor temperature to vary the temperature of the boiler output relatively high comfort & efficiency can be gotten out of the boiler.
It's highly unlikely that you would ever need anything close to 180F water, even on the coldest day if your 180F BTU/hour number for the radiators of 161,412 BTU/hour is the right order of magnitude. The graph on page 2 of
radiator sizing document I linked to suggests that most radiators put out 170BTU per hour per square foot:
So, if you have 842 square feet of radiator that's 143,140 BTU @ 180F, not 161,412, but it hardly matters- even 143KBTU/hour is literally FOUR TIMES the heat load of my (~2200ft house with ~1500ft of semi-conditioned ~65F) basement at my 99th percentile outdoor temp of 0F.
Unless you're on a high mountaintop in VA your 99th percentile design temperature is going to be higher than +10F, and could be as high as ~+25F if you're along the coast. My 99% design temp is 0F, and if I had your radiators I would never need more than ~120F water: My heat load at 0F is about 35000 BTU/hour, and with 842 feet of radiator that's 35000/842= 41.5BTU/hour per square foot. Looking at the graph, you can expect about 40 BTU/foot out of the radiators with 115F water. And since this is well into the condensing zone, that would yield 95% efficiency or better out of the boiler if sized correctly.
As it happens, I'm currently running my home's system at 130F max water temp, but in fact COULD heat the place comfortably with 115F water at 0F outdoor temps with some improvements to one of my radiant floor zones.) For you to actually
need 143K or 161KBTU/hour @ +10F outdoor temps you'd literally have to be living in a tent, or a very drafty 6000 square foot uninsulated barn, or keep some windows open all winter.
With that much radiation you have enough to run at very high condensing efficiency 100% of the time, but for optimum comfort & efficiency, size the boiler to the heat load, not the radiation. The water temp requirements don't change with the size of the boiler but with an oversized boiler it'll turn on/off more often, throwing away a fixed amount of BTUs with every ignition cycle and flue purge, adding up to lower efficiency and more wear on the boiler. With a right-sized mod-con boiler it would burn nearly continuously on the coldest days, but mostly at low to mid fire. It's very likely that even the smallest mod-cons are bigger than your design condition heat load, but as long as it's MINIMUM modulated output is at least 1/3 of your design heat load it'll be fine.