Quinoa has the advantage of storing for longer than potatoes, which were notorious for not lasting a full year. It is also distasteful to birds, which reduces some pest predation when compared to grain crops.
Quinoa doesn't yield as high per acre as potatoes, but then virtually nothing does. The rare exceptions don't grow in Europe anyway, being largely tropical crops grown under intensive irrigation and/or several crop rotations per year.
There's also the fact that quinoa won't be competing with wheat,
@metalinvader665 said you need to treat it before it's eaten. But to large extent I imagine that quinoa early on will be primarily used to cattle, this means it's fooder crops it have to compete with. The main fooder crop of northern Europe was beets, which demand good soil, as such a crop which can grow in rocky high acidity soil are a quite good completement to this, especially when it keep better than potatoes as you said. So I imagine it will first spread as a fodder crop, and only when the areas they grow in are hit by famine or warfare will humans begin to eat them, and slowly they will be mixed with different cereals in bread and porridges or mixed with barley (which was used as a kind of European rice). But as a fodder crop they will increase the animal calories produced, while also freeing land up used for other fodder crops. As example in Sweden the introduction of the Rotherhamp plough resulted in a loty land being freed up, which was used to feed work animals (as the new plough needed fewer animals), if quinoa allow the peasants to increase the land used, we would see the same results. At the same time this also means that the crop are introduced in new areas, so when people finally begins to eat it, it will spread fast.
We saw something similar in Norway, through the 17th-18th potatoes had spread there as a fodder crop, but it was only with the British policy of besiege the Norwegian until they died of hunger under the Napoleonic Wars, the potato was adopted into the Norwegian cuisine. Of course here quinoa are in a better position than potatoes as it can be mixed with other cereal. We saw that with rue, which was often mixed in the same manner. The Danish monopoly on cereal export to Norway could result in the Norwegians adopting quinoa relative fast as a crop for human consumption.
The result honestly if the crop spread successful to most of Western Europe in the 17th century, we will likely see a population increase in the Alps, this means more settlers to the Habsburgs Hungarian possesions, and we may see Slovakia and western Hungary get a wave of new German settlers first and later Transsylavania and the Military Frontier. in Switzerland increase population will suffer under the problem that their religious beliefs make it hard for the Swiss Reformed to emigrate to nearby countries. So they may lack a safety valve, the results could be a new wave of religious wars among the Swiss. We may also see a greater number of Mennonites leaving the country for especially America (Russian Mennonite mostly came from West Prussia and West Frisia).
In Scandinavia we will likely see the Norwegians adopt it as human food first and as such we may see a large Norwegian population explosion through the 17th-18th century, we could potential see norway make up half or more of Denmark-Norways population in 1800 (instead of 1/3), the results will be that Denmark can increase their army size, but we may also see Norwegian migrate to new areas, Kola and the White Sea could see a inflow of Norwegians (which also mean the introduction of the crop to the Russians), while internal in the realm the Norwegian may migrate to the Danish possessions in the North Atlantic. The result may be a similar assimilation of these into Norwegian culture as the Scot wave of settlers transformed Shetland and Orkney. My guess are that instead of Denmark-Norway having +2 million people in 1800, we will talk about 3 million people. A greater population for Denmark-Norway will likely result in Denmark investing in a bigger army and navy, but i doubt they will use it more, instead we will likely see increased colonial adventures. Denmark may be able to throw the Dutch out of the Gold Coast under the ARW (in OTL Denmark just use the opportunity to attack and enslave the Dutch allies, which had in the decades up to the ARW had attacked and enslaved the Danish allies), we could also see greater control of the Volta River (the Danes had already begun to move inland and setting up inland plantages owned by Danish merchants, mulattos and assimilated Africans), there wax also attempt to gain Danish territories outside India in Asia (the Nicobars) here the Danes may go after better territories. In West Indies Denmark may be able to expand the Danish West Indies by buying islands from others.
In Sweden the crop will likely become human food under the Great Northern War, and while it won't change that conflict, it will result in fewer losses for the Swedes and a bigger population boom through the 18th century. I would imagine the result of this would be increase settlement in Finland, but also that the greater population density result in greater assimilation of the non-Swedish speakers. So the result could be that instead of +3 million Swedes in 1800, we're talking about 5 millions and instead of 20-25% of the Finnish population being Swedish speakers we're talking about around 50%. This would place the Swedes in a much better position for conflict with Russia.