I realize that Omnichannel is currently only associated with the Customer Service module for 365. However we have had a request from a client to provide Omnichannel for a sales process on a web site which links into a sales CE 365 organization (so in other words an agent to guide the user through the sales process via a chat if need be).
Is it possible to add in the Omnichannel module for sales in any way and if not any sort of alternate solutions we could follow for this requirement?
No, Omnichannel is built on top of Customer Service so having this first-party app installed is a requirement detailed in the documentation. I recommend you to contact your MS Account Manager and discuss this topic with them as depending on your requirements you might also need Power BI/Customer Voice/Power Virtual Agent licenses as well so maybe it's worth to explore some cross-application licensing.
There're alternative solutions in AppSource like CafeX LiveAssist and a few others, please make sure you filter by application to make sure they will work with Sales.