I done a bit of research but wasn’t able to find anything unfortunately, its certainly one of them unique cases that you can never find any information on when you need to.
My guess, which is purely a guess and may or may not be factual, would be no, I would imagine that due to your account being frozen there could be some sort of regulatory reason involved in their decision to freeze your account, they may be legally required to stop any activity on your account e.g. closures, credits, debits, which a faster payment of your old account balance is made to your new account, which would probably be forbidden. They also may not be allowed to close a frozen account until they have completed their investigation and/or until they have received some sort of communication from the relevant authorities to unfreeze the account.
You would also be required to give the last 5 digits of your current debit card number to initiate the switch, which will also be inactive during this time, this may also cause some implications if they are unable to verify your card details.
My hypothesis only. However, the worst that could happen if you tried a switch is that it would be unsuccessful, the best that could happen is that it would be successful, Maybe I shouldnt be saying this but I would see no harm in trying it
In regards to funds transferring, as HoddzDJ said, it is only the funds in your current account that will switch. You would have to withdraw in cash or transfer the funds into your current account for them to be moved over with the switch, this would not close the savings account though you would need to close this manually. But due to the situation I suspect this wouldn’t be possible.
Hope I’ve been some help