In a word, YES.

Please note that the term "Events" may appear in place of "Activity", depending on the version of Remote Services you're using.

Activity/Event and Admin logs can be exported as .PDF files.

Whether you're downloading an Activity or Admin log, the default name of the file is "EventsLog.PDF". As with most Save or Save As actions, you can rename the file as you wish before download.
NOTE that logs can only be exported from the Remote Services website.
1. In the Activity (or Events) log, click the button at upper right on the web page.
2. A dialog box appears offering a choice of data to export. Options include events involving:
  • The security system itself (Arm/Disarm and Trouble/Fault events)
  • Devices (system-controlled lights on and off, etc.)
  • Your security panel's built-in camera, where applicable (primarily snapshots of someone disarming the system at the panel)
  • Times when the panel is synchronized with Remote Services
  • Rings and motion-detection events if you have a Wi-Fi doorbell
3. Make your selection(s) or select All.
4. Select a date range of events.
5. Click Export.
Note: As the warning message says, don't refresh the web page or log out of the site until the PDF is downloaded.

To export Admin logs, click the button.

With Admin logs selected, take the same steps outlined above.
Note: The button's tool-tip saying "show live events" simply toggles back to the system and device events described above.