There's a world of difference between a visual designer and a UX designer, not to mention a software designer (==architect). Most of the people here are more like UX designers, which in the context of a founder, means a "product person".
So if you're a product person (clearly yes), you qualify IMO.
You can go to school or be self taught... definitely, 'designer' is more like a mindset and skillset that you have to have the confidence/respect to own(you can be a developer, designer, business person all in one but very rare you can be great at all of them)... intentional behavior changed and impact definitely help qualify like real artists ship...not all are equal and we're talking about a very rare breed... if you read below the infographic we layout some unique characteristics:
-Clearly every designer isn’t meant to be a founder and probably shouldn’t be, (especially as some believe we’re spreading talent thin across too many little “me too” startups but that’s a whole other discussion). To be clear, we don’t mean “designer as the prima donna pixel-pusher” that you might be picturing. We also don’t mean “designer as the I Took One Class Called UX Fundamentals In Business School.” We mean an honest-to-goodness, experienced, craft-driven, product-focused, reflective practitioner who has learned to design by designing, who views design as a way of thinking about solving hard problems and is capable of building usable products with more than just beautiful aesthetics.[3] The word ‘design’ is so loaded nowadays and hope that our Designer Founders info cards will begin to clarify the impact of designers with various backgrounds in the context of early stage tech startups.
-Designer founders we’ve observed are consistently multidisciplinary and have cross functional skills necessary to make product decisions. They are fluent in the full design stack ranging from user research, product design, interaction design, information architecture, graphic design, to communication design. They may not be experts in all sub-disciplines of design but can get by on their own in the early days of their startup and attract specialists when needed. In addition, they have a thorough enough working understanding of technology and business stacks including agile programing and data-based marketing methods. Designer founders can move up and down the design stack and horizontally to technology and business stacks to do what it takes to ship and use data to justify their decisions when needed. Thus they are capable of leading both their product and organization through the design cycles needed to innovate. There’s a difference between a designer who can design a dashboard in a car and a designer who can design a whole car and how to drive it. Designer founders need to be able to do both.
I've never had the word "designer" on a resume, but I kind of feel like I'd qualify. But not sure.