When you add a Curve > Curve Spirals > Archemedian object (or other spiral objects as well), the default setting for Height is 0. In this case the spiral looks like a closed circle (ever wondered why Spiral creates a circle?).
However, if you set the height to a value <> 0 you will see that it's not a closed circle but instead an open spiral where the first and last segment lie directly on top of each other, e.g. here I've set a height of 0.1:
This means there is no need for deleting vertices to get an open curve - actually, if Cyclic would have been enabled, deleting a vertex wouldn't create an open curve. You would only have a vertex less and the rest of the segments would be connected to keep the curve closed. And after you converted the curve to a mesh, there shouldn't be any Cyclic option to enable anymore.