It sure is possible. I have been doing it for quite some time now and this would be a perfect situation for the Action Builder if coding in FormCalc is not your thing, but I can give you both.. I will use a sample form for the demo so if the lingo doesn't match up to your form, let me know or if you need an example. If anyone has anything simpler or I missed something, let me know. PM me if you want a sample form.
Create a new PDF and add in a second blank page and set that page to hidden in the Object field. Place a text field on page 1. Go to the Action Builder (in Windows go to the toolbar at the top, then "Tools" then select "Action Builder". The Action Builder is a great tool to add some extra functions into your PDFs with the preset actions. From the Action Tool box select the "Add New Item" from the top left of the box, right next to the trash can icon. This will create a new Action. There are 2 things for the Action: a condition and then a result. In the Condition section click the "object" link and then select the text field you put on page 1. Once you select the text field, the Condition box will change to "when text field TextField1...." and there will be 2 drop down boxes. With the condition set as "Is" put your password in the blank field. Then in the Result section select the drop down box and go to "Show/Hide an Object"and then select Page 2. What this will do is when TextField1 is equal to your password, page 2 will be visible. You can do this with not only a page, but specific elements within the PDF. So additional Textfields, pages, static text or other elements. One thing to keep in mind is what I like to call "foward/backwards logic" in that a user can enter the password to show the data, then remove it to hide whatever. Just go back through the Action Builder in reverse order that you did, where when TextField1 IS NOT the password, set the elements to hidden.
If you can do this via Formcalc, the setup would be similar, but instead of using the Action Builder you could do something like, create a numericField that has a number based password. On that field, go to your Script Editor, select "Change: from the show section, change the Language to FormCalc and then enter:
xfa.resolveNode("Page1).presence = "visible"
else xfa.resolveNode("Page1").presence = "hidden"
The bolded 1 is the password. The second and third lines cover what you want hidden or visible. So change whatever you want the password to, change the hidden and visible sections and then give it a try. You could even set this on a docReady show option as well to check that field when the form is opened if perhaps the first person saved the PDF with the hidden sections open. That way they do not need to enter the password every single time. Of course before they send it they should remove the password. Just be ready that whenever the user opens the form, even if they do not change anything, they will be prompted to save.