A short course of supervised growth hormone doesn't seem to affect natural production for someone with normal, age related decline. It's a youth hormone. After age 25 or so, you are essentially drawing down your reserve for the rest of your life. A healthy lifestyle and some specific measures can add a little back to the pool, so that it lasts longer.
Unlike testosterone, it can be optimized once, and then maintained to some degree, with specific, intense lifting, peak 8 cardio, eliminating all sugars post workout, and getting good sleep. These measures, while beneficial to production; on their own will never get you to optimum if there is a big gap to fill. Pure drinking water can help reduce calcification of the pineal and pituitary.
Cons are cost and potential side effects...which are often related to cost.
Trying to get maximum effects from a very expensive short course may invite overuse. This can lead to carpal tunnel and some other nasties, that may or may not resolve over time. JUST DON"T DO IT. The older you are, the slower you need to go.
It's hard to throw away a $1k pen that is half full, when the expiration clock starts ticking the minute you open it. It's also hard to find a doctor that will even discuss this subject with you...making it kind of a moot point.
I'll probably invite a flame with this, but...
If you and a bud were on a similarly supervised course, you could easily share one and toss it away empty.