I believe they can.
Wild Pokemon can have Pokerus, it's rarer, but still possible. Technically, all Pokemon in the Max Raid's/Dynamax Adventures ARE wild Pokemon. That said, the virus is 3x rarer than a shiny.
"Pokerus can be caught by battling a wild Pokemon that has the infection. The virus is about three times as rare as a Shiny Pokemon in the wild. Once a Pokemon catches it, the word Pokerus will be shown in the Pokemon's summary menu." https://www.ign.com/wikis/pokemon-sun-pokemon-moon/Pokerus
That is as of Sun and Moon. Although, the overall battling system hasn't changed much since then.
Having said all that, wild Pokemon can be infected with the virus, but it's 3x rarer than a shiny. Wild Pokemon examples: In tall grass, wild area, fishing, etc.
Like shinies, wherever you can catch Pokemon, there is a chance. (This is excluding Shiny-Locked Pokemon)
(Quick Side-Note: I had tested this out all yesterday and ONE Pokemon had been infected with Pokerus out of the hundreds I battled)
Hopefully that helps, and apologies late answer.