What effect does hyperinflated lungs (caused by asthma) have on the circulatory system, if at all? what possible symptoms may manifest as a result of this condition?

Usually none: The label is often cited when reading a chest ray of someone in poor asthma control. It means the air sacs in the lungs appear like over inflated balloons. These findings are usually transient & improve as the asthma event comes into control. Mild stress on the right side of the heart is usually well tolerated with no outward symptoms.