According to this technet article, Windows 7 does not prevent logging in, does not reboot, and does not cripple normal applications while in an unactivated state. This means that you can run long-running applications as long as you'd like, so long as you're not trying to do one of the precious few things that are prohibited while in this state (e.g. using Windows Update for optional installs).
There will be a longer than usual login time (you have to dismiss a notification dialog), your desktop wallpaper will disappear, and you will be unable to install optional updates, use KMS, or access genuine Microsoft downloads (programs that require a genuine copy of Windows to download/install).
The relevant information regarding this experience follows:
Notifications
The purpose of the notifications-based experience is to differentiate
between an activated (genuine) from an unlicensed (non-genuine) copy
of Windows in a way that maintains computer functionality, such as
logon, access to the familiar desktop, and so on. Reduced
Functionality Mode (RFM) is not in Windows 7 or Windows Server 2008
R2. Instead, both operating systems have a notifications-based
experience. This new notifications user experience means that
computers that are not activated during their grace periods (initial
activations and those that result from hardware changes) or that fail
validation may provide the following user experience:
After logging on to the computer, users see a dialog box reminding them that Windows must be activated along with options to activate now
or later. If users do not interact with this dialog box within two
minutes, the logon process continues normally.
In the notifications state, Windows changes the desktop wallpaper to a solid black background, displays notifications in the notification
area indicating the activation state, and displays dialog boxes
showing actions that the user must take.
In the notifications state, users have access to the full functionality of the installed version of Windows, with the following
features disabled:
a. A computer configured as a KMS host responds to KMS client requests with an error message that KMS has not been activated.
b. Windows Update downloads security and critical updates (optional updates are excluded).
c. Optional downloads requiring the online validation service—also referred to as genuine-gated downloads—are not available.
The computer must be activated for it to leave the notifications
state.