No. Based on the community answers, Affinity Photo’s Curves adjustment does not currently include Photoshop-style black, gray, and white eyedroppers.

Closest alternatives in Affinity Photo are:

• the Picker tool in Curves, which lets you sample a tone in the image and drag up or down to brighten or darken that tonal area
• the dedicated White Balance tool or White Balance adjustment layer
• setting white and black points through other adjustments/tools

So if you specifically want the three Curves eyedroppers found in Photoshop, the answer is no. But you can still achieve similar correction manually using the Picker tool plus white balance and black/white point adjustments.