Unfortunately no, Google does not allow the pop-up box to be running in Google Sheets' mobile/tablet app. It will work only if you use mobile web browser with the steps below:

1. Go your mobile/tablet Google Chrome or any other web browser.

2. Click on the 3 dots icon on the right.

3. Make sure the Desktop site is checked. (It may be called as Desktop mode or any other name in other web broser)

4. Go to sheets.google.com using the same page.

5. Make sure that the page is same as the middle picture, if not repeat step 3.

6. Look for your Sheet and click on it.

7. The passcode pop-up should be working as usual.