You are asking whether IPv4 “fails over” to IPv6 when IPv4 is unavailable. Yes, it sort of does if you look at it from the wrong angle, but it is actually the other way around.
When IPv6 is enabled, it is preferred over IPv4. So in actual fact, IPv4 doesn’t “fail over” to IPv6. Rather, if IPv6 is unavailable, it “fails over” to IPv4.
Your question asks specifically about IPv6 mail servers, but this behaviour is universal. HTTP, FTP, IMAP, you name it. If a website is both IPv6– and IPv4–enabled, your browser will prefer the IPv6 version (assuming you have IPv6 connectvity). If you are sending mail to an IPv6–enabled mail server, it will go over IPv6.
(As to whether it will try again over IPv4 if your IPv6 fails I cannot answer at this stage — not tested it myself, unfortunately. If this is an issue, you could use two MX records — one that points to an IPv6–only hostname, and one to an IPv4–only hostname.)
If you IPv6–enable your mail server, but still keep IPv4 enabled (e.g. on Postfix you would set inet_interfaces = all, not inet_interfaces = ipv6), then you will be able to send mail to IPv4 and IPv6 mail servers, as well as receive mail from IPv4 and IPv6 sources.
This wasn’t part of your question, but does pertain to IPv6 mail servers: currently none of the major DNSBLs (e.g. Spamhaus) support IPv6. While I haven’t seen a single piece of spam originating from an IPv6 address, be aware that the only spam preventative measures you can take are keyword–based.
Let's use the term "IPv4-dependent applications" to refer to applications that use IPv4 literals (e.g., 10.10.10.1) or are coupled to IPv4 in other ways that break functionality on a IPv6-only hosts. IPv4-dependent applications will not work on IPv6-only hosts.
Many applications that do not use IPv4 literals and rely on DNS names will work with no problems on IPv6-only hosts.
NAT64/DNS64 is mechanism for IPv6-only hosts to reach IPv4 hosts on the Internet. This transition method is needed because the majority of Internet content is reachable only via IPv4 transit.
I recommend reading Experiences from an IPv6-Only Network. You'll find a great deal of material on which applications break on IPv6-only hosts.
Best Answer
People require an IPV6 address or something like a proxy to allow them to see an IPv6 site. IPv4 and IPV6 are different stacks, so it will be the case that users of IPv4 only stacks will not be able to reach your IPv6 only site.
With respect of an alternative to an http/https proxy server at another host, its possible a VPN provider can provide you with an IPv4 address across IPV6 only infrastructure - not sure if thats of much help.