Not if you don't want it to. AceSpy has an advanced user filter where you can enter Windows username(s) which won't be monitored. To setup the filter, go to Settings > Filtering Options > User Filter. Then enter an entry for your Windows username *exactly* as it appears to Windows.

In the event that you only have one username for all user of your computer, you can go inside AceSpy and click EXIT at the bottom and Yes to confirm. This will stop all recording until you reboot.