Nope, the public address will be different
I'll put their statement as-is in a quote,
We are using ARK public keys that are associated with your ARK public address to generate a PHANTOM based address which will receive the forked credit.
Source:
https://phantom.org/2018/08/28/phantom-zinc-claim-guide%e2%80%8a-%e2%80%8aark/In the images from the guide I linked above, it's obvious that the address has changed. In the first image you can see an ARK address starting with "A" and in the last image an address starting with "P". So the Phantom addresses will be starting with "P". Only the pass-phrase (aka private key) stays the same.
Btw if you use a Ledger Nano, don't put any key you have from your hardware Ledger there, just add the network settings for Phantom and then insert your Ledger (and maybe restart the wallet)
There is no contact email no address no names and the contact form on their website is not working!