Does Podcast Connect support redirected RSS feeds?

I'm afraid I can't advise any further. It's a bit odd, because a 301 redirect should work independently of whatever ntype of client is involved - browsers, or different services like Podcasts Connect. The redirect, if a 301 is being used, should be seamless,

The 'itunes:new-feed-url' tag should work but requires there to be a valid feed in place at the original URL.

By the way everything should be ideally be https so that's unlikely to be the issue.

You could try asking Support, though I can't promise you'll get a response. Go to https://itunespartner.apple.com/en/podcasts/overview and click the 'Contact Us' link at the bottom of the page.

I can't give you a positive answer as I've never had occasion to try, but if it's a properly set up 301 redirect it ought to work.