One would have to think about it and investigate. Say, they might confiscate your laptop with thunderbird and your mail archive but they probably wont delete your webmail account or forbid you from using it. At least I imagine if the point is to gather information it doesn't include deleting it or taking control of it? If they really want to delete your things I imagine one could create an append only webservice.
Preserving some things (without hiding anything) is better than nothing.