Yes. All gasoline breaks down over time when exposed to air, with some of the volatile chemicals evaporating and what is left behind slowly forming goo... E0 and E10 alike do this (the 10% Ethanol just has the added bonus of attracting water and all the fun that can ensue from that.)
A good fuel stabilizer bonds to that nasty oxidized fuel before it can form goo, converting it into stuff that can be burned by the engine. This works for a while (like over the winter), but it is not magic (leave it for a year plus and it doesn't matter whether you have stabilizer or not).
Not all stabilizers are created equal, and some are just dumb gimmicks. Watch some of the "Taryl Fixes All" Youtube videos testing stablizers in small engines to get a sense of this. I use Stabil 360 Marine or Chevron Techron Marine stabilizer in all my equipment (the Stabil does pretty well in testing, and both contain PEA fuel system cleaner as well).