You could consider Joseph Andrews a picaresque novel since a picaresque novel contains, by definition, an almost exhausting collection of adventures.
As you might recall, Joseph, Adams, and Fanny go through many ordeals. Before Joseph even meets Adams, he’s also already pursued by multiple women—including a Lady and a maid—and left for dead in a ditch with no money or clothes.
Again, that’s just the beginning. Once Joseph meets Adams, more adventures arise. Another maid is attracted to Joseph. Adams seems to prevent a sexual assault. Shortly after, Adams is accused of murder.
Again, the accumulation of episodes met the criteria of a picaresque novel.
Yet you could claim a key component of the picaresque novel is missing from Joseph Andrews. “Picaresque” comes from the Spanish word “picaro,” which means “rogue.” Some definitions of “picaresque” explicitly call for a roguish but likable hero.
The Collins Dictionary states:
A picaresque story is one in which a dishonest but likable person travels around and has lots of exciting experiences.
However, the Cambridge Dictionary says that a picaresque novel is a
a type of story in which the main character travels from place to place and has a series of adventures.
If you go by the Collins Dictionary definition, the first definition, you might run into trouble linking Joseph Andrews to the picaresque novel. Joseph might not have been born into affluence, but I think you’d have a hard time arguing that he’s “dishonest.” You could say the other characters are dishonest and unprincipled, but those other characters are just that: other characters.
To review: If you think of a picaresque novel as a series of adventures, you could say Joseph Andrews is a picaresque novel. If you think of a picaresque novel as a series of adventures specifically undertaken by “a dishonest but likable person” then you might have a harder time considering it a picaresque novel. Joseph is not dishonest. If anything, you could claim Joseph is almost too virtuous.