Yes, it's possible. Vim already features that general style of code completion built-in, under the name of Omni completion.
The default installation doesn't allow for auto-invocation, but if you install this script, that allows it to happen.
Note that, depending on the language you'll be working with, you may need additional scripts to handle auto-completion for that language, and may even need to change the auto-invoke script to recognize when to invoke the completion. Since you haven't said what programming language you'll want to work with, it's a bit hard to say if you need more than this, but I recommend checking the help file.