Yes, all fish can, but more importantly what caused it? Until you identify and correct the issue that caused this, it will simply happen again, or the fins will not heal
FYI - Fish fins take a while to grow back especially for Angels - We are talking months for Viel Angels to grow completely back if they were removed completly.
I saved an old Angel and he had 50-60% fin loss. I am simply allowing him to regrow his fins on his own and uping his protien in his diet. I have had him for a month now. They have grown back maybe 1/2" already