There was a time when EDI really could have been considered to be separate from IT. The specific disciplines were different in that the people who managed the EDI systems needed to understand more about the language of X12 than about the specifics of connecting a computer to the company network. But with the growing demand for full transparency and visibility across the supply chain it isn't enough to have gaps between the technologies that run the company. Your EDI functions need to be connected to your logistics and to your ERP. They also need to be connected to your marketing and catalogs. And they need to connect to your ecommerce functions. 

And because of the speed of demand and the multiple ways to sell, all these things need to be connected. I don't mean connected in the way things were connected years ago - by batch updates run overnight. They need to be connected in real time so that things like product availability can be viewed in real time. When a shopper orders a product through one of your retailer's web sited that is going to be drop shipped from your own warehouse, that web site should show at least whether the product is available at the time of their order. Notifying the buyer their item is backordered 2 days later will kill a customer relationship for you and for your retailer.

There are many ways to integrate your EDI with your company's ERP. Chances are that your EDI software provider can deliver components that will set up a direct link between your applications. If your combination of accounting (ERP) and EDI are not able to be connected, I would advise looking for a combination that does deliver this kind of connection. Putting off the transition will not make things better - it will only make the problem bigger and more difficult to resolve. Check this article that Buzz posted about ERP Integration for some clarity if you don't know where to start.