Maybe, maybe not. It will die sooner or later from deprivation of quiescence. Plants need to get ready for a winter of weather that doesn't allow growth: too little sunlight of short days and low intensity of the sun passing through more atmosphere via a steeper angle and little or no water because of long periods of freezing conditions and frozen roots that can't supply water inspite of winds that would dehydrate the plant if the leaf cells allowed ordinary transpiration to take place. They are programed by the conditions of autumn progressively limiting these processes so that by the end of autumn, the tree is ready for winter. Take away the progressive changing conditions and the plant will just mope. Take away the rest period and it will die. Very few species that are hardy can survive "no winter". Boxwood, some Elms, (like Chinese), and a few others, but they do poorly and by the end of winter look crummy and you'll be sorry you have to look t them.