Not really. Because historians are not even sure what Knud it is.
There are several contestants to being Knud I - Gnupa and Hardegon/Hardeknud, being two. There is a reference to a Gorm Hardeknudsson and that is likely Gorm the Old.
To make matters even more confusing, a Knud who styled himself as Knud IV, may actually have meant that he was the fourth son, not the fourth Knud.
And even more confusing. In the period before Gorm the Old united Denmark there may have been up to several chieftains named Knud!
DK was only a lose kingdom before Gorm the Old.
Sometimes a chieftain or local king was strong enough to unite all or most of Denmark, but when such a king died or was defeated, the kingdom fragmented. And sometimes it was probably divided among several sons.
But there had been several strong kings in place before Gorm the Old, Because his wife, Queen Thyra, strengthened the border-wall, Dannevirke. Marking the border (militarily it was actually a trip-wire) between the Danes and the Saxons. So that fortified line had been build before Gorm the Old was king.
That confusion is basically the reason why Gorm the Old is considered the first official Danish king, and not least because his son, mention Denmark, on the stone commemorating his father. That mentioning of Denmark is the first in an official context.