That is roughly the reverse of what has tended to happen in recent years as the normal technology transmission belt has been inverted. But the process would be something of a return to past adoption patterns, in roughly the same way that "software as a service" and cloud computing now "returns" us to an earlier era with some resemblance to a mainframe or centralized model of computing.
In the past, software and hardware innovations tended to be "discovered" in the universities then commercialized first in the enterprise buyer segment. Over time the price and feature set would be "de-tuned" for the mid-market, with adoption then spilling over into the small business market and then sometimes even in the consumer market.
Now some observers say targeting the enterprise "edge" can stimulate buying in the broader consumer market.
What is different, and might enable this to work, is that Web apps are much easier to adopt in an enterprise environment. Less customization is needed. Also, the user interface, designed for consumer use, tends to require less training, again reducing the hassle factor for adopting in an enterprise environment.