Grunts can earn Edge, too. There is no indicator that you need an Edge Attribute to accumulate Edge. And for Spirits, itīs actually spelled out that they canīt earn Edge (or rather, donīt want to?

). Right now, deciding that autonomous Drones
canīt get and use Edge is just as much of a houserule as deciding that they can.
And deciding that they canīt is
obviously a very bad rule, because it further guts the premise of the Edge mechanic: Two Drones shooting at each other? "Yeah just ignore AR, DR and everything else.
Streamlining, baby!"
Apart from that, Iīd say itīs generally a good practice for GMs (apart from any houserules that may or may not be needed here) to simply spend any Edge a Drone, Grunt, Critter etc gets right away on the very test that granted it. It reduces bookkeeping and itīs also a good a idea realism-wise.