Why not?
The Varyags crossed the continent of Europe in half no time. Portaging over divides and rapids, fully vulnerable to ambushes by the locals. The local Finns and Slaves were numerous - they grew the same plants, herded the same animals, rode horses, had the same metal tools and arms... Varyags united them nevertheless.
Imagine a comparable timeline...
Around 1010: Thorfinn and his 160 souls settle in Vinland as per OTL. They have some quarrels with Skraelings as per OTL. But he manages to resolve them by judicious combination of appeasement, violence and divide-and-rule. The Beothuk leave the small Norse enclave at peace, and the Norse trade iron tools to them. (North American Indians knew metal - the native copper of Lake Superior was traded far and wide - but not smelting.)
1010... 1050: the Norse make several exploring expeditions southwards. They find warmer climate, nuts and hardwoods in New Brunswick and Massachusetts - and they also find numerous Indians growing maize. They also sail up St. Lawrence up to Lachine Rapids like Cartier, and find the same. Some more shiploads of settlers come from Greenland and Iceland to Newfoundland.
1050: Snorri Thorfinnsson and a number of Norse leave the Vinland colony and sail to settle at Hochelaga. Hochelaga becomes a centre of trade in North America - the Viking iron competes against (and to some extent complements) Lake Superior copper. Snorri establishes alliances with the neighbouring tribes. His friends - a few Norse and a few Indians - travel far and wide around Great Lakes and Eastern Woodlands, exploring routes and establishing alliances.
1080: Thorstein Snorresson leads a large war party of several Indian tribes and maybe a few tens of Norsemen (most of the still few Norse settlers of Hochelaga stayed home, as they have trade, ironworking and herds to tend to, and too few Indian apprentices to do it all) past Lakes Ontario and Erie, and reaches and conquers Cahokia. He is proclaimed Grand Duke of Cahokia by his retinue.
The new Grand Duke goes on to lead a number of expeditions in different directions - up Ohio, to Lake Superior, up Missouri, and down to Mexican Gulf. Udel principalities are founded, some by local Indian chiefs who ally with Grand Duke, some by Indian allies in his train, some by his Norse friends and some by Metis.
1110: The new Grand Duke, let´s call him Powhatan Thorsteinsson, acting on the information about the fabulous rich countries around the southern sea, has a number of ships built on Mississippi, and after reaching the Gulf of Mexico again, sails west around the coast. In Veracruz, he hears about the weakening Tollan far inland beyond the mountains, but realizing that his small force would be too vulnerable to ambushes in the long road through mountains and could not haul back all the loot if successful, he decides agains. Instead, he continues east, lands in Yucatan and undertakes the shorter, level-ground march against Chichen Itza.
What next?
How is Powhatan Thorsteinsson getting along with the Althing of Iceland? And how will the Bishop of Skalholt react?