Yes we invest it, and we do have about 2K in the cash account--I believe that's a requirement of the particular HSA my employer provides. It automagically sweeps anything above that into a separate investment account.
As a caveat though, I'll state that we've never, not even once, made a claim on it in the 3 years we've had it. We pay all our health care bills out of pocket. We've maxed out our allowed contributions to the HSA, my employer kicks in a bit more every year, and the balance is approaching $20,000 over that 3 year period.
Our plan is to use it as another tax deferred retirement account. We try to keep all my health care bills so that we can eventually make the tax-free withdrawal claims, which I understand can be made whenever we want with no expiration. Certainly if we had financial hardship and could not afford to pay my health care, we would dip into it, but knock on wood my family has had no major health care costs other than the occasional physicals and minor illnesses, dental/orthodontal work, etc.
I would put it in index funds if the plan offered that option, unfortunately they don't so it's in an equity growth fund. We actually didn't start investing until May 2012. The share price of that particular fund has gone up about 20% over that time (not that that's necessarily any indicator of future performance of course).
