You're the DM.
If you want to roll this in as a plot hook, then go for it! A few things to keep in mind, though, based off planning I have done for this campaign.
Hunting Artus is a big deal, and the Zhents know how many people are looking for Artus. They aren't going to assign hunting him to just anyone. It would likely be only highly-trusted operatives involved in this hunt.
It may be appropriate for that PC to be assigned the mission later, once he's done some other things to build trust with the Zhentarim. He was just recruited. That would be sort of on-par with a police officer coming straight out of the academy, instantly being snatched up by the FBI, and put in charge of hunting down someone at the top of the Most Wanted list.
More likely, the PC may be given some "things to watch for" that interest the Zhents. He isn't explicitly given such a ridiculously important mission, but he's given a sketch and told "if you see this person, report to your superior." I would also, for flavor, make up a few other things that are 'of interest' to the Zhents that the player may never encounter.
Then, the 'mission' of catching Cimber can grow organically once the player encounters him, reports back to their superior, and starts being fed orders on what to do.