Technically – even proof of feasibility of such non-integrated process is barely attainable IMHO. Let’s imagine blue-sky: Instead of using integrated and proven tax procedure TAXUSX and having ERP interfacing with Vertex through standard RFC…Well you probably still need external tax calculation activated in ERP to avoid maintaining jur codes in ERP. You need custom RFC to e-commerce to populate interface TAXDOC00 in the same way RFC_CALCULATE_TAXES1 does. You need custom (Zxxxxx) tax procedure with requirement(s) ABAPed in a way that conditions for 6 levels of possible taxes in US are picked from e-commerce system. Your tax jur code will need to be brought from e-commerce in the same way that RFC_DETERMINE_JURISDICTION does. You will need to break the link between new Z tax procedure and external tax system if copied from i.e. TAXUSX. Hope that reporting will pick everything up as expected. And then imagine thunderstorm - returns, credits etc.
I may overlook or not know something but it appears that simply integrate and have tax jur code and amounts coming from Vertex is WAY easier. Key point to me is that tax reporting will be done from SAP. This is not an easy way mostly because if you do business in multiple jurisdictions (read: states) it is much simpler to do your US tax reports in Vertex/Sabrix/Taxware than from SAP. There may be exceptions but still.
I could not agree more with Jelena and would suggest having both e-commerce and ERP integrated with Vertex.