I haven't been able to verify the information you have given here. The only Louis (or Lajos) Kovacs in the 1920 Census for Detroit was single, immigrating in 1914 from "Sabocs Slk," which I assume is Szabolcz megye, now Slovakia. His age (29) is also way off
The only Kovacs which seems to fit your description at all in the 1920 Detroit census is Louis Kovacs, age 32, married 9 years. He immigrated in 1907 and was a lodger, living without his wife.
Have I somehow missed the entry you located? Can you give more details? Where do you see "Kraso, Slk"? There was no Kraso, but many places beginning with Krasso, now all in Romania.
There is also another Kovacs in the 1920 Detroit Census that matches some of your information, but that is for Anton Kovacs and his wife Elizabeth, children Irene, Rose, Anton Jr., and Elizabeth. Anton immigrated in 1906, Elizabeth in 1904. They were naturalized in 1914.
The 1910 Detroit Census, however, gives two possibilities. One is Louis Kovacs, age 32, married 9 years, immigrated in 1907. However, he was a lodger, living without his wife.
Another possibility is Louis and Ersi Kovacs in the 1910 Manhattan NY Census. Louis was 29, Ersi 26, and they had a son Louis, 2 months. They were married in 1907. However, their immigration dates of 1906 and 1904(?) suggest they were married in the U.S.
The most direct reference I found to your family was the World War I registration of Louis Kovacs, address 47 Keller, Detroit, born November 21, 1878. His wife's name was Elizabeth. This would fit in with the 1910 data for both the Detroit and Manhattan entries, but suggest a much earlier immigration date.
There is a Bekes in Hungary, both a village and a county, but there is no "Aran." Many villages begin with "Aran," but none in Bekes. Could it possibly be "Arad"? This city is now in Romania, as are most of the villages that begin with "Aran." If this information is solid, it does suggest that Louis and Elizabeth met after immigrating, since most people in Hungary married someone who lived close by.
It would help to know where your data come from and how reliable it is. What information do you have that you are absolutely certain of?
If you can provide further details, I would be happy to do some more searching.