Running 2 sites that use ASP.NET Webforms (in case you don’t know it, an 18-year-old technology that has a lot of problems and only runs on .NET Framework). I don’t think it’s a good fit for Caddy ;)
Caddy can sit in front of it as a proxy, no problems. It can terminate TLS for you, and your existing server can do the rest of the heavy lifting for serving your site.
