Can 3rd party apps be ran in background?

[Velerona]

I have an app called Teamviewer for both my iPhone and my iMac & I want to be able to have it running in the background of my iMac all the time so I can connect to it from my iPhone anytime I want. Otherwise I have to open the program to let it get connected to the web. I'd like for it to always be on without any notification of it being on like dock or taskbar menu. Here is what it looks like when it is up and running. The little grey window in the upper right corner is semi transparent when your mouse is not on it. I do have dock dodger installed so the app icon is not docked but I want both of the windows seen to be able to be gone and it still remain connected. Is this possible? Thanks for any advice.

 

[flat five]

⌘H will hide an app.. (or app menu-> hide _or_ rightclick app's dock icon->hide)