Is it possible that I need a relative URL to get the linked image indexed?
No, if you make the URL relative, all that will happen is the requesting user-agent has to pre-pend the current domain to the specified location, so unless you have the wrong domain or file path in the URL it doesn't matter if it's absolute or server relative.
Using an absolute URL will cause the user-agent to request exactly the location indicated.
Server Relative (full path from the root)
Using a server relative URL will cause the user-agent to request the location after pre-pending the current root/domain, so on example.com the requested location will be http://example.com/the-path/to/the-file.ext
Directory Relative (path from the current directory)
Using a directory relative location is one of the most mistake prone ways to do things, because the user-agent will request the location after pre-pending the current path. So:
If the user-agent is currently at http://example.com/ and sees the-file.ext it will request http://example.com/the-file.ext
If the user-agent is currently at http://example.com/the-path/ and sees the-file.ext it will request http://example.com/the-path/the-file.ext
If the user-agent is currently at http://example.com/the-path/to/ and sees the-file.ext it will request http://example.com/the-path/to/the-file.ext
People often run into issues with directory relative URLs, especially when moving files to different level directories and forgetting to change the directory relative URL to "point" to the actual location of the file they are trying to indicate should be requested from the new location of the page it's linked from. (I definitely do not recommend directory relative URLs personally.)
Either absolute or server relative should be fine as long as you have the actual path (/the-path/to/the-file.ext) correct and the domain name correct in the case of absolute, or the user-agent is visiting your site in the case of server relative.