Your coins are fine. You don't understand how Bitcoin transactions work at all. If you are interested in Bitcoin and intent to get invested in this experiment, you should read about the basics. Then you will understand why expecting your coins to be lost because your wallet was offline at the time of reception is an absurdity. Do yourself a favor and research this tech, you'll be much better off and highly increase your potential at success.
I totally get that i don't fully understand how the Blockchain works and I am trying to understand little by little.
My concern was not that my wallet was offline at the time of reception. I already know that doesn't matter. It was that when I created my Armory wallet and the addresses generated it was saying Node Offline at the bottom right and has not been online even after attempting to troubleshoot and I had sent bitcoin to an address created by Armory.
How can I get my Armory wallet to say node online? Will the blockchain know that the wallet address belongs to my desktop wallet once I get things sorted within Armory?
Any troubleshooting steps would be appreciated.