Integrating a CodeIgniter ordering app within EE

[eluser]Unknown[/eluser]
We are looking to build an ordering app (shopping cart without payment processing) within an EE site. We have setup a weblog to handle all aspects of the products and their management with custom fields.

Here are the main features:

1. The users would have to register/login before being able to "Request A Quote". So we need member management.
2. The client would like users to be able to "Request A Quote" by adding products and their options/details to an "order". So we need a session to store the products in the order.
3. Upon submission the details of the "Quote Request" are emailed to an admin and stored in a quote request table.
4. The user needs to be able to view past "Quote Requests".

There are some other features, but these are the main ones needed to help understand the scope and answer my questions.

1. Has anyone out there done anything like this? (had to ask
2. Since we don't need payment processing, could I integrate another shopping cart with EE to do the job?
3. Could I develop a basic app in CodeIgniter and integrate it with our EE site?
4. Are there any other suggested approaches/hacks/work-arounds to our challenge?

Thanks in advance for any help!!
John Peele

[eluser]Michael Wales[/eluser]
EE has an eCommerce solution built-in, the rest of this sounds pretty easy using default EE modules (Member Management, developing a stand-alone entry form).