Is it possible to use k-means algorithm with just one vector
Certainly possible. You can think of it in the way you described but I would say it just becomes an adaptive thresholding assuming a bimodal distribution: We admit that there are two main modes in the data and we try to identify those by grouping the values around the means of the clusters. These groups form clusters. The means are positioned such that each element contributes to the average of the cluster it belongs and thus creating a mode nearby. 
It is almost sure that the minimum and maximum will go to separate clusters.