The straightforward answer to this question is yes. Call of Duty: Vanguard has striking connections and references to Black Ops Cold War and Modern Warfare. For starters, we are aware of Task Force 141 from the Modern Warfare games. As such, Vanguard is based on the creation of the first Task Force unit itself.
Furthermore, we have previously witnessed how the ultranationalist terrorist leader, Imran Zakhaev, from Modern Warfare, appeared in the Black Ops Cold War campaign. This linked BOCW and MW to some extent. Another major aspect of these games that link them together is Warzone.
Zombies from Treyarch’s Black Ops appeared out of oblivion and led to the destruction of present-day Verdansk. As per the lore, players are currently experiencing a flashback of what happened in Verdansk during 1984. Once again, the city will collapse, and we will move further back in time to Warzone Pacific on the new map of Caldera.
The link between Black Ops and Vanguard was revealed via a trailer prior to Vanguard release. In the Pacific cinematic trailer, Adler and team meet with Butcher, the creator of Task Force, inside one of the German Bunkers in Verdansk.
This is unlike the last generation of Call of Duty games, i.e., the original Modern Warfare and Black Ops. Infinity Ward and Treyarch developed those games separately, and there was no visible connection between the two CoD subsidiaries.
This seems to have changed as Activision has moved towards a more inclusive approach. This combined approach has had a major impact on the games’ sales. Activision integrated the fanbase to sell games from various studios with much less effort.
The reboot and integration of the franchise’s best titles have been extremely successful. It is evident from how well the new Call of Duty games are performing according to sales standpoint, despite being subpar with their predecessors.
For more on the upcoming Call of Duty Vanguard, check out Why are there no factions in CoD Vanguard? on Pro Game Guides.