Does my battery health go down if I leave my iPad on for a while

With your iPad sleeping, routine background tasks continue to run. As such, your battery will continue to be depleted, albeit at a much slower rate than when being actively used. If powered-on, but unused, you might expect the iPad to delete its battery at about ~10% of its battery capacity per day.

Even if fully shut-down, you can expect the battery to deplete a little every day. Your iPad does have an off-switch that totally disconnects the battery (instead the iPad has a soft-off condition - where the iPad electronics are almost fully shut-off) and, as a consequence, the battery will drain a little every day. In addition, all rechargeable batteries exhibit a phenomenon known as “self-discharge” - that will result in full discharge over an extended period.

Generally, it is unnecessary to fully shut-down your iPad unless you have no intention of using it for many days. Even if you do fully shut-down the iPad, its a always a good idea to charge the device every couple of months - as doing so reduces the chance of irreversible damage to the battery through deep-discharge.

Batteries - Maximizing Performance - Apple