Yes. You'll see that an update check is done before OpenLiveWriter is started:

C:\Users\username\AppData\Local\OpenLiveWriter\Update.exe --processStart OpenLiveWriter.exe

However, you will not get any type of message. You can check on the version number by:

• Click on File
• Click on About

You'll see the version number in the dialog box.

Note: if you want to turn off AutoUpdate, see the tutorial on Registry Keys