JWs will claim that it is possible to know Christ and have a personal relationship with him.
We all know that JW's claim a lot of contradictory things. For instance, JW's almost universally claim Jesus is their Mediator (for prayers). But the WT's position and official church doctrine is that Jesus is Mediator ONLY for 144K Christian believers over the past 2000 years.
Of course their is no biblical definition of a Mediator being the bearer of prayers like the rank and file JW's believe. Scripture says that Jessu is the "Mediator of the New Covenant" the one "for the forgiveness of sins" in Mt. 26: 27-28.
Similarly, Of course JW's are going to claim they have a personaly relationship with Jesus. How can you claim to be a "Christian" religion and not claim that?
But can a person have a personal relationship with someone else if they never spoke to them even once?
I don't think so. JW's would never talk directly to Jesus in prayer. So, no; they have no relationship with Jesus at all.