(I am hoping one of our bailiff experts will be along soon. I am not one, so all I write here is surmising possible scenarios as to what is happening.)
So if I paid now would I be refunded if the TEC rule in my favour
I think that you have misunderstood the role of TEC (- see
https://www.ftla.uk/announcements/charge-certificate-cases-under-the-traffic-management-act-2004-no-original-pcn/ and replies #10, 11, 12 above)
All TEC do is order the Couyncil to cancel the OfR and Charge Certificate, which makes the original PCN out of time, hence the need for a re-issue of the PCN if they want to continue enforcement, placing you in the position you would have been had received the original PCN in a timely fashion.
Birmigham will, no doubt, have or will issue a fresh PCN, hence my concern that if they send it to the original address you could be back to square one. So please check with them what they wish to do and if they have the right address for you.
Others will be be along to correct the mistakes I may have made.