Can tests be run across both web apps and desktop?

My company bought the Desktop license only.  I would like to be able to run tests that span both desktop and web apps.  We have many desktop and web apps that are integrated.  A current manual lifecycle test we run consists of entering data into a desktop app, then checking that the data was transferred to one of our web apps.  Then performing steps in the web app and making sure those changes are seen in another desktop app.  This goes on across multiple apps.  Does this sound like something that could be automated if we had both the web and desktop license for TestComplete?