Can we use plants in place of gutters?

If you dont want to use plants, and you one option would be place gravel at drip line. You would need some kind of fabric under the gravel to prevent washout.

Install a Gutter and Small RainWater tank to Get Water for Your Garden Where i Live All our Drinking Water is Collected from the Roof into a Water tank. No Chemicals,or Chlorine ,Floride Etc

You just need to figure out what works best for you to keep the runoff from the ground. Gutters will need to be cleaned of leaves, seeds, etc. to keep them running right. If you don't you will have the water coming back from wherever the blockage is. With the huge trees in our yard they are constantly filling our gutters with flotsam jetsum and I have water running over the gutters all year. It is a constant battle.

Adding plants close to the wall of the house can create a problem of retaining moisture right up against the foundation. Adding topsoil next to the wall and grading it away from the wall should help, but if the force of the rain is strong enough to wash the soil away you probably need a professional drainage solution, or replace the gutter.

You might also add some rain chains, and then put one of those concrete troughs underneath to direct water away from building.... they are about 18" to 24" long. I would do pea gravel and put a bender board to keep it in place. https://www.google.com/search?q=rain+trough+and+chains&client=opera&hs=FBg&tbm=isch&tbo=u&source=univ&sa=X&ved=0ahUKEwjivvvkwYLUAhXEv1QKHSUqB-8Q7AkI3wE&biw=1366&bih=629

http://www.target.com/p/emsco-splash-block-granite/-/A-17441606?ref=tgt_adv_XS000000&AFID=google_pla_df&CPNG=PLA_Patio+Garden+Shopping&adgroup=SC_Patio+Garden_Top%20Performers&LID=700000001170770pgs&network=g&device=c&location=9033057&gclid=Cj0KEQjw9YTJBRD0vKClruOsuOwBEiQAGkQjP4-Sgh9mVb6D1tRseCdkymPOkso0PvXFN-iuyfahDowaAqXQ8P8HAQ&gclsrc=aw.ds