Is Balsamiq a "Stage 1" product and part of the initial design process for producing a mockup/design for a client or can I be used solely for this purpose?
The biggest thing to consider is stakeholder expectations and your end goals as a designer. Depending on what your goals are Balsamiq may be more or less valuable than other tools.
Example 1: Your have a simple site requirements and want to impress your client with graphic design. In this instance Balsamiq is probably not going to be as useful as Illustrator or Photoshop.
Example 2: Your customer has a complex site or app and has asked that you improve its functionality. It might take several iterations of working with the customer to define what "improved functionality" means. The focus in this instance is not on the graphics but on the structure of the site. In this case you want to use software that lets you iterate as fast as possible. Balsamiq is very lightweight. If you are capable of doing this with illustrator then by all means but often times the graphics and colors can get in the way of discussing core concepts like navigation.
Example 3: You client identified some very specific problems with their site. You are trying to show very specific and complex interactions for improvements for a site such as click animations. Balsamiq is not appropriate. You may need something like Axure or another interaction tool.
Depending on your role, relationship with the customer, and contract you can explain the purpose of the mockups you are presenting and how they fit into your process. In these instances mockups are very appropriate because they are the simplest way to communicate the ideas. If a client doesn't like an idea you do not have to spend hours adjusting styles. If you are worried that the lack of fizzle will worry your client you can pick a single page and do a full mock up to help the client see how the mockups relate to the finished design. Some designers use mockups to get all the major requirements settled before laying out a full mockup. It's important to note that while some processes tend to work better than others that there is not a defined set of rules for how you go about your process. You may have to adjust to deal with specific expectations from customers.
If I understood correctly, you want to know if Balsamiq is considered a proper tool for presenting wireframes to a client.
Short answer is: Probably yes. Balsamiq is a very good for simple to medium complexity interfaces.
However, it depends really on the functionalities of what you want to show. If you need to explain interaction, you might want to consider something like UXPin, that works quite nicely with different states and allows you to save templates to re-use throughout the project, or even something like Axure if you have a bigger project with lots of components.