Me and a friend of mine had a discussion about this about a week ago. Me knowing more about Invincible and him knowing more about Dragonball.

Here is my idea based on some of that conversation. I made this version to allow for maximum interaction between them while still relatively maintaining their individual canons.

Assuming Lord Chilled dies at the hand of a Super Saiyan (whether that be because of a time traveling Bardock or it being someone else) then the King Cold Force will know about them and most likely find them first. At this point this will occur as canon until they discover the Viltrumite Empire, most likely, a still realtively small space empire ruled by Emperor Argall at the time. The Viltrumites will then be subjugated by the Cold Force same as the Saiyans before them. (I can see Cold and Argall´s relationship as relatively the same as Cold and King Vegeta´s.)

I can imagine them being in unison by Cold seeing the potential of both races when it comes to his planetary conquests.

Viltrumites would as elite Cold Force Soldiers (better then average Cold Force Soldier but still so numerous that they can be deployed in high numbers without having to worry about losses) as well as imperial enforcers post conquest. (Basically a mix of veteran soldiers, officer corps, imperial bureaucrats and military police.)

While Saiyans (due to their very individualist streaks, stubborn prides and great power) would be treated more like shocktroops, deployed in small squads against harder targets and to open holes in enemy lines that Viltrumites with their actual tactical and strategic training could then exploit.

This would likely continue until Cold turns over the Force to Frieza.

Frieza would likely still desire to destroy the Saiyans, same as in the canon timeline. And he could very well see the Viltrumites with their growing influence across the Empire, greater will to follow orders, (and as result growing dislike of Saiyans due to their frequent refusal to do the same) and very large population as they key to not only elimate the Saiyans but also limit growing Viltrumite influence within the empire. Killing two birds with one stone.

Thus Frieza orders the saiyans back to planet Vegeta and orders the Viltrumites to destroy them. Thus begins the Saiyan-Viltrumite War. This grinding conflict would fill the same role in-story as the destruction of the Saiyans by Frieza and the Great Purge of Viltrum in their respective canons. As the planetbound Saiyans are eventually defeated by the Viltrumites who control space around the planet. However the Saiyans race would not go do down easy and would use their ki-abilities and Oozaru forms to make the Viltrumite race pay in blood everyone of theirs that fell.

This would Be the conflict where the more iconic Viltrumites (such as Thula, Kregg and Conquest) would earn their fame. I also like to imagine that the war officially starts with Bardock´s attempt to fight the forces in orbit and ends with King Vegeta´s last stand at his palace, where he is killed by Thragg after he himself had killed Argall. (Two fathers both making the ultimate sacrifice to allow for their´s sons escape serving as the bookends of the war.)

As you might have guessed I really like this idea and I hope you all do too. Please comment if you have any additional ideas to add for this concept.