Just staring at the old South Dakota road map I have, it looks like a logical part of the route. It would appear US 77 went straight north on what is now SD 11, then multiplex with SD 50 to the place marked Junction City on the SD map, then north on the road which parallels I-29 to the east. (When you are actually there, you can generally see this road from the interstate.) However, I can't find a source which says that part of SD 11 is US 77 and I can't find any maps online which would say something one way or the other.
Yes.
http://www.lib.utexas.edu/maps/topo/250k/txu-pclmaps-topo-us-sioux_city-1955.jpg
http://www.davidrumsey.com/luna/servlet/detail/RUMSEY~8~1~212134~5500242:Shell-Map-of-North-Dakota,-South-Da?sort=Pub_List_No_InitialSort%2CPub_Date%2CPub_List_No%2CSeries_No&qvq=q:Publisher%3D%22Shell%2BOil%2BCompany%22%2Bdakota;sort:Pub_List_No_InitialSort%2CPub_Date%2CPub_List_No%2CSeries_No;lc:RUMSEY~8~1&mi=0&trs=2
A weird thing about this segment is that it just ends at the city limits of Elk Point. I have no clue why there is no connection to BUS I-29, but I guess it's just one of the reasons why South Dakota is wonderful.