No, you can’t. A bechamel sauce by definition is made with milk thickened with a roux.
You can make a roux and add water to it, but what you’ll get won’t be bechamel. It will be pretty flavorless and it won’t have a great texture. If you don’t want to use dairy you can make a velouté instead. It’s essentially the same process, but instead of using milk you use either chicken, veal, or fish stock.