No power drain to fear. A simple status led will consume less than 1 mA. Its impact on battery life is neglictible, a 9V battery could keep it lit for more than 10,000 hours.
On piezo preamps like Fishman, a LED is often used to indicate you must change the battery. It turns on after the battery is considered drained.
Remember these Pulse Pink Floyd CDs ? They blinked for years and were powered by a single AAA battery.
Yeah, I don't know why some people think an LED will drain the battery. If installing an LED, control the amount of current that it draws with a resistor. 2k2 is pretty standard for this usage in effects pedals, but you could go higher too. You don't need a switch, just wire it up in parallel to your onboard electronics and use the plug as a switch the same way those do.