for stereo calibration (extrinsics), yes. you need to know (measure/calculate) the size of those squares. that determines the absolute scale.
for monocular calibration (intrinsics), no.
you’d also benefit from the pattern spanning a larger fraction of the picture. the smaller it is, the more difficult it is to estimate lens distortion. you can do that with a larger pattern, or by getting closer to the camera. mind the focus of the camera. the pattern will get blurry if you get too close. you can’t change the focus because that commonly affects the focal length and lens distortion.
using a computer screen of any kind is a good idea though. it’s a lot more accurate than most printers.