Yes they are possible. The ESA's ExoMars will be highly autonomous

It can move autonomously, making its own decisions and building up its own navigation maps, and the scientists just tell it where to go. It can go up to 100 meters a day, and also drill autonomously too. For details see Robotic Exploration of Mars: ExoMars Rover

And I'm sure we'll have faster and more autonomous rovers in the future.

Also - the main bottleneck is not the light speed delay, but the bandwidth. At present scientists can only communicate back and forth in one or two short sessions per day.

If somehow we achieve broadband communication with Mars, then they could communicate back and forth many times each day and the rovers could do as much in a day as they currently do in weeks. There are ideas about how to do it, probably involves dedicated communication satellites in orbit around Mars.

With broadband communication you could also use "artificial real time"

That would speed it up hugely again, maybe close to the capabilities you'd have with humans in orbit, though that would be the most immediate of all, to contorl rovers on the surface using humans in orbit around the planet.

See my Soaring, Buzzing, Floating, Hopping, Crawling And Inflatable Mars Rovers - Suggestions For UAE Mars Lander

To Explore Mars With Likes Of Occulus Rift & Virtuix Omni - From Mars Capture Orbit, Phobos Or Deimos

Case For Moon - New Positive Future For Humans In Space - Open Ended With Planetary Protection At Its Heart