I use Gmail for email in my Google Chrome browser. Is there a way to make Gmail appear as an application that I can choose using the application switcher invoked with Cmd + Tab?
Browser tabs cannot be added to the application switcher; only running applications can. However, there are various native wrappers around Gmail (by Googling, I found Kiwi and Mailplane for traditional Gmail and Boxy for Inbox by Gmail, although there are plenty others out there) and services that will simply construct a native app that is merely a web view containing a specified website (i.e., Gmail) (these include Fluid and Applicationize, though, once again, there are many others). These native apps (or those generated by these services) can and will appear in the application switcher when active.
Note that I am not affiliated with, and have never used, any of the services mentioned herein.
Fluid lets you create a Real Mac App (or "Fluid App") out of any website or web application, effectively turning your favorite web apps into OS X desktop apps...your chosen website has a permanent home on your Mac as a real Mac application that appears in your Dock.
Gmail is even one of the examples they show in the video, and it supports features like badging the application icon when you have new messages.