The plugin uses standard form POST request to send the email, in your case for the user it would look like page refresh. I’ll see what I can do about it to make it more user-friendly.
I think it’s possible but it’s very unsafe. Anyone entering your email (assuming they know you may be a customer) would receive a link and will be able to manage your Stripe profile, subscriptions, cards, etc.
Links to Stripe’s customer portal would expire if not visited once in a while, so whatever solution / form generator you use, you can’t create a permanent link and just send it to your clients with their orders.
I faced this problem on my website and had to create a plugin that retrieves link to customer portal from Stripe upon user’s request. Here it is if you are still interested: Get Stripe Customer Portal Plugin.