My only access to computer is my Samsung epic cell phone. My storage is getting full because I take a lot of photos. If I send them to Gmail & archive them. Will this free up some storage space in my phone even though I keep my Gmail app on my phone ?
Short: Yes. You can send your photos as email attachments and delete them from your phone. It will free up your phone memory. But there are other options which are better than this.
You can use cloud storage facilities to back-up your data and access them anytime and anywhere you want. More details about widely used cloud services can be found in this answer.