Should an ammeter always be connected in parallel with a component?

No, an ammeter should never be placed in parallel with a component - it should always be placed in series, so that the current through the component is measured.

If you place an ammeter in parallel with a component, you create a short circuit around the component. Depending on the rest of the circuit, you could damage the circuit, damage the ammeter, create a fire, etc. You certainly will affect the current through the component, and that is not what you want to accomplish.