At least in this Florida case, the answer is no. I've linked to the Episcopal church press release, and a place where one can read the decision. The decision is constitutionally based. Essentially, the court said it would not get involved in deciding internal matters where there was a hierarchical structure -- which the Episcopal church is. (Note: Some California cases last year came out differently, based, as I understand it, on California property law.)
http://www.episcopal...
The Episcopal News Service says:
A Florida state judge has agreed with the Episcopal Diocese of Florida's claim that it and not a group of dissidents owns the property of the Church of the Redeemer in Jacksonville.***
Judge Karen K. Cole ruled *** that Florida state law requires her to accept the diocese's determination of who is the rightful occupant of a congregation's property. She wrote that the state law defers to decisions made by the "highest ecclesiastical authority" in a denomination structured as a "hierarchical church." Such a denomination is one that is organized into governing bodies of hierarchical ascending jurisdiction, Cole explained.
Six other breakaway congregations had reached an agreement to amicably separate.
The case is Episcopal Church in the Diocese of Florida, Inc. v. Lebhar, (FL 4th Cir., April 27, 2007).
I have no idea what this means for the Virginia lawsuits. However, as I understand it, the Florida result is the general rule (to which there are exceptions).