Not totally clear on what you are asking, but if the questions is; does giving out a referral code to an existing user in hopes that they would refer another work? My experience (largely in B2B software) is not all that well, at least not without some sort of incentive. Even if your user is super satisfied with the product/service you are providing, simply giving them a code to give another person doesn't necessarily drive them to make the handoff. Now, two things.
First, if you either incentivize the existing user with say a discount on his next bill or a free goodie, then he'll be more likely to do it... Even better, if you do that, plus give the referred user some kind of benefit, like a discount on his first bill, free trial or other goody, then it can work rather well.
Second, all that said, know that referrals in general are gold. You should test and do whatever you can to get referrals. Generally @Leads360 we found that providing really high quality customer service (more so than even the best product) lead to referrals. To that point, our sales people worked in tandem with customer service in this way.
Whenever a CS person realized they gave a great customer experience they would let the sales person know and they would then reach out to that customer while still warm from the nice touch and simply ASK for a referral. I was always surprised when we could get referrals simply by asking. I like to stick with 1 referral at a time, just ask for 1 person to be email connected with, don't overwhelm them with the statement "hey, can you refer your friends and colleagues to us", be specific. Something like "I see on LinkedIn you're connected with John B from ACME corp, I'd really like to speak with him about our product, would be willing to make an introduction for me".