E cadherin is downregulated when cells undergo EMT, and this is partially regulated transcriptionally, and by all means accelerated endocytosis might help too (I don't know if it has been proven). However, it is hard to imagine how an E cadherin could be endocytosed when it is tightly interacting with an E cadherin from the adjacent cell (i.e. an adhesion belt). It is likely that dissociation of cells is mediated by cleavage of the extracellular portion of the cadherin from the transmembrane domain and what is then left may dissociate from the protein adapter that links it to the cytoskeleton and can then be endocytosed.
I would read the following article to get an idea about the formation of extracellular soluble cadherins after cleavage from the transmembrane domain..
Jimmy, the loss of E-cadherin is sufficient to induce the transition from adenoma to invasive carcinoma, which implies an EMT-like process (Nature. 1998 Mar 12;392(6672):190-3.; Cell. 1991 Jul 12;66(1):107-19.).However, in HCT116 cells, loss of E-cadh is not sufficient to induce N-cadh or in vitro invasion (J Cell Sci. 2010 Apr 15;123(Pt 8):1295-305. doi: 10.1242/jcs.061002. ). E-cadherin is definitely not a simple EMT marker, it is clearly an actor!