The Germans maintained a deep faith in Enigma throughout the Second World War--a faith that aided allied codebreakers. What would the effects on the Allied codebreaking if the Germans believed, rightly or not, that a fully intact Enigma machine with codebooks and wheels had been captured intact by the British.
Nothing.
The Germans were not so stupid as to believe that no Enigma machine would ever fall into enemy hands. They knew that it happened at various times.
They recognized that if that happened, the enemy would be able to read all Enigma traffic on the key used with that machine - until the captured keys ran out in a month or so.
The Germans believed, not without reason, that it was impossible to solve an Enigma key by mathematical induction, and that the number of possible settings for an Enigma (in particular the four trillion possible plugboard settings) made it impossible to solve a key by brute force trials of all large numbers of keys.
They overlooked the mathematical tools developed by Polish and British cryptanalysts, which enabled them to break Enigma. They also overlooked severe operational errors in their use of Enigma (Cillies, the Herivel Tip, Parkerismus, repetitive messages) which greatly assisted the Allies in breaking keys. And they did not imagine the electromechanical bombes which allowed the Allies to test far more possible keys than the Germans expected.
However, there are other ways the Germans could have learned that Enigma was compromised. In 1939-1940, the core of the Polish Cipher Bureau worked at Vignolles in France under the aegis of the Deuxième Bureau, in full collaboration with GC&CS at Bletchley Park. The break into Enigma in early 1940 was a joint achievement, and of the several thousand decrypts in the next three months, about half were produced at Vignolles.
Vignolles was occupied by the Germans in June 1940; the codebreakers had evacuated, leaving no clues for the Germans. But what if they had failed to clean up everything? What if the Germans discovered a file cabinet of ciphertexts and decryptions? Or worse yet, a a file of notes on the decryption
methods?
The Deuxième Bureau staff who supervised the Vignolles center did not go off to join Free France; they remained in the service of the Vichy government. In fact they had the Poles resume work in southern France, from September 1940 until November 1941. Thus the Vichy government (or men nominally subordinate to it) held the Enigma secret. They kept it - but what if they hadn't? What if one of the French supervisors lost his only son to the British attack at Mers-el-Kebir?