In short, the answer is No.
Facebook's Platform Policy states:
You must not store or cache any data
you receive from us for more than 24
hours unless doing so is permitted by
the offline exception, or that data is
explicitly designated as Storable
Data.
The offline_access
extended permission actually has no affect on whether you can store any data, you may have confused it with the offline exception
, which is as follows:
Offline exception: Applications that
run on a device controlled by and
possessed by the user -- such as
desktop or laptop computer, mobile
device, or other embedded device --
can cache user data received from
Facebook for more than 24 hours only
when Internet connectivity is
unavailable or it is impossible for
the application to run. Such data can
be stored on the client device but not
a remote server, and cannot be made
available to the developer. Cached
data older than 24 hours can be
displayed to the user (or otherwise
used by the application) in lieu of
updated data only until an update is
possible, and in no case beyond 14
days after the last update.
So this means that all you are allowed to store, unless you are covered by the offline exception
, are the following data fields:
User data you receive from Facebook that you can store indefinitely:
uid User ID
nid Primary network ID
eid Event ID
gid Group ID
pid Photo ID
aid Photo album ID
flid friend list ID
listing_id Marketplace listing ID
page_id Facebook Page ID
proxied_email Placeholder email addresses for your users
notes_count Total number of notes written by the user
profile_update_time Time that the user's profile was last updated