The answer seems to be a firm "maybe".
Remember aminophylline.Once a mainstay in the treatment of asthma and COPD exacerbations as well for longer term therapy in the form of various oral preparations, it now generally considered a third line medications almost about as likely to be used as the 12th man on the NBA bench in a close game.
Interestingly, one of the purported ways that aminophylline was thought to exert a therapeutic effect was its inhibition of PDE3 and PDE4. Now a new drug, roflumilast, is being studied to treat obstructive pulmonary diseases is also a phosphodiesterase inhibitor.
Recently four phase 3 clinical trials were published in the Lancet.See here for a brief summary.
The four trials involved 4500 patients;two lasted six months and two for one year. A decrease in exacerbations was shown as was a slight increase in some parameters of lung function.These statistically significant outcomes occurred in patients who were already taking a long acting beta agonist or an anticholinergic ( Tiotropium). Nausea was the most common side effect.