Can I use my Plusnet login on a GSM connection if my line goes down?

[#1]

First the background. The BT phone line to my house runs through a tree and gets damaged occasionally. Last time, I was without broadband for over a week. Since I run a mail server on my Plusnet Business connection (static IP) this was a problem. It seems nobody wants to sort the tree problem until the connection is lost - but I'd like to avoid losing service when it happens.
I have a mobile 3G wireless router (TP Link M3530) and I am wondering if I can use this as a temporary backup if my line goes down? I need to keep my static IP for the mail server, unless I subscribe permanently to a dynamic DNS, which seems overkill for a problem that may not happen. I also need to forward the mail server ports to the right machine, and the TP-Link doesn't seem to offer port forwarding. My normal broadband router is a Billion 7800 and has a EWAN socket. I also have available a Raspberry pi with wireless dongle and Ethernet.
If I pick up a 3G connection on the TP-Link, connect over wifi to the Raspberry pi, then by ethernet to the Billion, can I connect from the Billion using my normal Plusnet broadband credentials, and get my usual static IP port forwarding in the Billion? I can see at least two potential issues but am at the limit of my knowledge - first, is it possible to have a public IP connection from inside a private subnet? Second, would my Plusnet login work if I'm not on a Plusnet line?
Alternatively, if anyone knows how to get a tree removed from the phone line (or vice versa) without having to wait for it to create a fault...

[#2]

I would think that would be impossible (using same IP ect as your fixed bb ) on  your mobile, as your using someone else's network  and they will allocate an ip address  which most likely will be via CGN  so you will share that IP with others  there isn't any way i can see how you could connect to plusnet's radius servers from a mobile device

[#3]

Thanks for the info - that's even worse than I feared. If the G3 connection is CGN then it's no use for hosting my mail server, even with a dynamic DNS.

[#4]

You'd be better off setting a backup MX provider on your domain for if/when this happens again (they're also useful to configure anyway in case you have server / power outages). I've not used any of them personally but something like http://www.backup-mx.co.uk/ would do the job.
Basically these services accept emails for your domain and then periodically try and re-send them to your server.

[#5]

I'll also second Matthews suggestion.
When I was an IT manager, we ran our own email servers but had a secondary backup "catchall" account with an ISP and any mail that couldn't get routed to our primary MX record would fall back to the ISP mailbox. You would get the occasional mail in there when it should have gone to the main server but generally it worked well.
Do you have a friend or colleague who run their own mail server ? You could possibly use each other as a backup should your primary connection fail.
Certainly using a mobile which will almost always have a dynamic IP address will not work.

[#6]

Thanks for the suggestions - appreciated. I did have an MX backup through Plusnet, until they scrapped the service, and I might have to find a replacement, but MX backup just saves the emails for when I'm back online. Last time I think the line was down for over a week so I was hoping I could find an alternative way to access the mails. I did originally have them forwarded by the hosting company (and could then forward to a webmail account if necessary), but they sometimes had several days of backlog, and they also insisted on spam filtering which I couldn't opt out from or add whitelists to, and I lost mails. Thanks anyway.