If your application is targeting the full .NET Framework: no you cannot (natively). It needs to be installed on the client machine. There are third party tools available like TurboStudio* which should enable you to accomplish this. My guess would be that slows down the experience for the end user as well. And it will do so each time the application runs, instead of only the first time.
To install the .NET framework straight from your ClickOnce install How to: Include prerequisites with a ClickOnce application.
Before you can distribute prerequisite software with a ClickOnce application, you must first download the installer packages for those prerequisites to your development computer. When you publish an application and choose Download prerequisites from the same location as my application, an error will occur if the installer packages aren't in the Packages folder.
To add an installer package by using Package.xml
1. In File Explorer, open the Packages folder.
2. Open the folder for the prerequisite that you want to add, and then open the language folder for your installed version of Visual Studio (for example, en for English).
3. In Notepad, open the Package.xml file.
4. Locate the Name element that contains http://go.microsoft.com/fwlink, and copy the URL. Include the LinkID portion.
5. Paste the URL into the address bar of your browser, and then, when you are prompted to run or save, choose Save.
6. Copy the file to the root folder for the prerequisite.
You can now distribute the installer package with your application.
*Taken from this SO post: Running .net based application without .NET Framework