Absolutely, you should invest your HSA funds! Currently, I have an HSA, my husband has an HSA from a previous employer, plus an HSA with his new employer. We invest everything we can. I hope we get the point that we don't need to touch the HSA funds to be reimbursed for health stuff, but right now, we do take funds out regularly. Mostly our contributions cover the current costs, though, so we aren't touching the invested funds, only the newly deposited cash.
HSAs are quite literally the best retirement fund out there due to the tax advantages, and if you have good investment options within them, go for it.