Sam,

I'm not sure what you meant by "spread the business".  But the short answer is yes, an analyst often will interact directly with business stakedholders to elicit requirements.

The first step is to identify which stakeholders you want to elicit requirements from.  These wll be people who are know as being the expert in the area you are trying to understand.  Some companies don't like their star business people "wasting their time" by sitting with or hanging on the phone with the business analysts.  This isn't a great start if the is the attitude of the corporate decision makers.  But their are other ways. 

Often projects with have people who represent the business.  They may not be the expert for a particular area, but they generally have a broad overall understanding of the business process. When there is something they don't have the answer to, then they will go back to the true business expert.  The idea is that these business representatives can answers most of the BAs questions and the business experts won't be bothered very often.

You need to determine what level of interaction with the business is expected within your company and project.

Hi Sam,

As a BA, you need to understand the boundaries of your scope of work (what have you been contracted to do).  As you gather requirements, you shall at times uncover areas of potential sales (e.g. up sale).  Potential sales opportunities are passed on to the Sales (or Business Development) Team and no additional work for the BA on this area is required.  Doing otherwise shall be considered out of scope work and may lead to scope creep, which at the end of the day shall delay the whole project.

Duke