No.
Width is how wide something is. Length is how long something is.
Don't confuse something that is easily rotated with something that isn't. For example, you might always say that a ruler is 12 inches long and 1 inch wide, no matter which way you rotate it. In this case, the length is typically used as the longer of the two dimensions. Something static, like a door, is a different case; with a door, the width measures how wide something is. Architects are required to be very aware of door widths for different rooms because of building code requirements. And as pointed out above, it may be wider than it is tall.
Your claim that the width of a sink is always the shortest dimension is false. Sink dimensions cater to the installer, who generally includes a plumber but almost always includes a millwork installer, and those people think in terms of length of a countertop (workspace). So for a sink, the length is the distance parallel to the length of the countertop (side-to-side as you address the sink from the front), and the width is the front-to-back measurement as you address the sink (but it's the width across the millwork). This dimension may or may not be greater than the length; it depends on the sink.