Fishing off a ship doing 20 knots... No.
Fishing off the after end had the chance of a fishing line getting wrapped round one of the shafts. Not allowed or necessary.
Any fish magically caught by rod and line off a ship at that speed was a particularly stupid fish and, if given to the galley staff (who had umpteen different kinds of fresh fish in the cold rooms to choose from) they would have binned it and given you sole meuniere instead. If it was on the menu...
My company Canadian Pacific had two tankers moored close to oil rigs as shuttle and storage tankers, and they caught vast numbers of fish. The company forbade it as - typical HSE that was coming in in those days - there was a risk of infection from it... What the difference is between a North Sea cod caught by a rod and line, and one caught by a trawler - gutted, chilled, handled, sold, transported and acquired by a ship chandler and shipped to the ship by helicopter, was difficult to conjecture. Needless to say, it was ignored.
On another ship at anchor off Capetown our Chinese crew ignored the same directive and caught hundreds of fish, which were then placed on boards to dry out in the sun. The stink may have been perfume to Chinese olfactory organs, but not to ours!
Then again up the St Lawrence and (topically for this forum) stopped in ice (-21°C air temperature), the crew hauled in a 6lb plaice which stuck to the deck as it landed. The chefs chipped it loose with a shovel and I went into the galley to see how it was going. The plaice steak in the pan was part cooked at the bottom and still twitching at the top. Freshest fish ever!