Second of the Scharnhorst class, Gneisenau was an unlucky ship, meeting her demise as an active combat ship due to an unlucky bomb hit in February 1942, after the Channel Dash. However, perusing her Wikipedia page, this comes up:
After arriving in Brest, Gneisenau was the subject of repeated British air raids. The first attack took place on the night of 30–31 March, and a second occurred on 4–5 April. During this second raid, a 227 kg (500 lb) armor-piercing (AP) bomb narrowly missed the ship. As a result of the attacks, the ship was moved out of the dry dock and moved to the harbor. On 6 April, Gneisenau was attacked by British torpedo bombers, which managed to score a single hit. The Bristol Beaufort that struck the ship was piloted by Flying Officer Kenneth Campbell. The torpedo struck Gneisenau in the vicinity of the rear main battery turret. Some 3,050 t (3,000 long tons) of water flooded the ship and caused a 2 degree list to starboard. The flooding also disabled several components of the ship's propulsion system. The explosion caused significant destruction to the side plating as well as the starboard and centerline propeller shafts. The concussive shock also caused widespread damage to the ship's electronic components. A salvage tug came alongside to assist in the pumping effort. Following the attack, Gneisenau returned to the drydock for repairs.
Three days later, on the night of 9–10 April, several British bombers dropped around 25 t (25 long tons) of 227 kg AP bombs on the ship, four of which hit. All four hit the starboard side of the forward superstructure. Two of the bombs exploded on the main armor deck while the other two failed to detonate. The attack killed 72 initially and wounded 90, of whom 16 later died of their injuries. The bombs slightly damaged the main armor deck and caused some structural damage on the starboard side. It was decided to make alterations to the ship while she was drydocked for repairs; these included the installation of fourteen additional 2 cm anti-aircraft guns and six 53.3 cm torpedo tubes amidships. The aircraft hangar was rearranged, and the catapult that had been mounted on top of it was removed. The length of repairs and modifications precluded participation in Operation Rheinübung, the sortie by the new battleship Bismarck in May 1941. The British continued to attack the ship in drydock, though no further damage was done. On 6 February 1942, a bomb fell close to Gneisenau, but caused no damage.
What if the bold bits don't happen? Note that the RAF Brest raids were notoriously difficult and innacurate and so I do not think it unlikely that Gneisenau dodges damage in April. After all, Scharnhorst, which was also in Brest during the same period for engine repairs, suffered no damage at all in these raids and only was damaged in July when she went to conduct speed trials in La Pallice.
I suppose that, while Gneisenau is in harbor, the Kriegsmarine will still modify her along the lines in red above. This should still allow her to participate in - you guessed it - Operation Rheinübung in May. As it was Raeder wanted her to participate so this is in line with OTL Kriegsmarine planning.