Doesn't seem like it. Using the interactive board on the website I was able to produce a solution that only revealed numbers.

Creator here. No, you can arrange the puzzle pieces to make dates that don't exist, like Monday February 31. Actually there may be "impossible" dates, because I didn't check for them, but I guess all combinations of days of the week, day of the month and month are possible. And also many non-dates, like 1, 2, 3. But good point: alle possible dates have at least 1 solution. Disclaimer: I sell these puzzles for a little more than the raw material.

Was just about to link to this one!

I thought the same thing, but it seems that certain dates would make it so there is one square ("rhombus") and one (non-square) rectangle (e.g. Feb 15).

So rather than 3 rhombuses – or 3 squares – perhaps it's 3 squares of 1 square and 1 rectangle. (Perhaps the positions of the puzzle pieces make it such that it truly is 3 squares)!

Announcing new Diamond Shreddies!

https://www.youtube.com/watch?v=bccNH82DIo0

https://www.youtube.com/watch?v=hF_2yHXD_CU

(and...neat puzzle...nice job, creator!)