Yes, this is possible. You can do this using colors from the Copic palette, or using custom colors not currently in app.

To set a Copic background color:
  1. Open the Settings menu.
  2. Under Workspace > Background, select Custom Color.
  3. This will open the Copic color wheel. Choose a color from the wheel to set it as your background.

To set a custom background color:
  1. Use the color picker to pick your custom color from a photo or screenshot.
  2. Draw a stroke with the color you want to use.
  3. Select the stroke and tap the paperclip in the pop-up to copy the stroke to the iOS clipboard. This also copies the color to the color clipboard on the color wheel.
  4. If you don’t want it hanging around invisible on your drawing, tap the trash icon to delete the stroke.
  5. Open the Settings menu. Under Workspace > Background, select Custom Color.
  6. The inner ring of the color wheel that appears will have the color on your clipboard (next to black). Tap this to set it as your background color.