I wouldn't... you say security is a concern: if you consider that
there's a risk of a scrote breaking into your neighbour's house and
climbing up into his roofspace in order to enter your house, do you
think a couple of sheets of plasterboard will impede his progress for
more than a few seconds?!

Really more a privacy than full on security issue then I guess.

Also, I don't know how big your loft hatch is but that might well be an
issue when it comes to taking sheets of plasterboard up there; at least
you're going to be restricted to using small bits only.

Hatch is about 2.5ft square so pretty big by all accounts I guess.
Thanks.