Rover

Yes it is possible and there are a few different ways to approach the problem - most involve considerable Word skills and effort to be able to implement it in a very user friendly way. You could do it with checkboxes actually in the document itself but I think the best solution may be to use a VBA UserForm in a macro enabled template (.dotm).

Do you know any VBA (the macro language in Word)? The best solutions will require you to be able to work with that.

I'm thinking the link that PrincessApril provided is not directly applicable to your question so here are a few other links that might be worth a look and show some of the options and complexity in getting to your end goal.
Using VBA to allow a checkbox to hide/show content in Microsoft Word - Stack Overflow
Can you use a Checkbox control to toggle hidden text in a Word 2010 document?
Is it possible to remove/hide text in a Word document based on checkboxes? If so, how do you do that? - Quora
How to Create a Microsoft Word Form That Auto Hides Text When Checkbox Is Checked? | It Still Works

Note that in all these links, the users are 'hiding' text rather than not putting it in the document. It is much easier to delete (or hide) content than it is to create it. Your template should contain all the possible content and the macros then hide or remove the 'not selected' content. Hiding it can be better if someone was to change their mind and want a way of getting a section back again. Deleting it makes that harder.

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Andrew Lockton
Chrysalis Design, Melbourne Australia