The answer to your question is no. As of this writing, the Affinity Photo curves tool does not have an equivalent to the eyedroppers present in Photoshop's curves tool.
You can, of course, set white balance (dedicated tool) and white & black points via other means.
The eyedroppers have been a highly requested addition for years amongst AP users, but they have not shown up to date. The following is pure speculation on my part, but I wonder if adding them to AP might get a bit too close to patent infringement.
I'm any case, as I mentioned above, there is a dedicated tool and a dedicated non-destructive adjustment layer for white balance. Setting white and black points is nothing more than telling the program "make this point white/black." That can be done with the Picker tool that Pete mentioned above: just click on what you want to be white ànd smack it to the top, or what you want to be black and smack it to the bottom. The Levels tool in AP is also quite good for this task.