my timeline Manstein in Africa's first installment explores this; and indeed has the Axis bait the RN into a trap where they lose a lot of ships in coordinated air strikes
the germans had several rl oportunities where they where skirting around the edge of their problem;
1. intel captured in poland
2. certain british air and sea movements being suspiciously well timed in 1940 (even beyond radar)
3. rommel was utterly convinced his signals network was compromised (although he didn't understand why) so he did a ton of stuff by courier/radio silence or just ignored radio orders from rome and berlin... he could have read the problem differently
4. rommel had several opportunities during different battles where he could have captured 8th army hq which might have left enough documents to put him on the track that his signals network was compromised
5. kesselring nearly pushed the 5th army back into the drink during operation avalanche, if he overran them or compelled a hasty evac of the army hq staff, its possible he could have captured vital documents that could have let him on to ultra... ditto for anzio
6. the allies did telegraph their punchs a bit obviously in some battles (like during the battle of averanges and the battle of mortain) which could ahve set off alarm bells
7. 7th panzer had an outside chance of being overrun in 1940 which would have let a fair amount of enigma gear fall into British hands which might have increased german paranoia about its viability
the question is how aggressively do the germans respond
periodically they got paranoid about their signals security and would increase the difficulty of the enigma patterning system (ie extra wheels) which would put the allies out of the loop for several months; but wasn't a long term solution
the pod i used; and like for the scenario because it solves two birds with one stone (ie the germans find out they have a problem, and develop a solution to the problem):
namely the germans and italians conduct an operation where there is minimal coordination between the two armies; and the german element of the operation gets roughly handled due to their surprise not existing whereas the Italians have a walkover... operation felix or maybe hercules could have produced a situation like this that might have set off alarm bells, and the solution is obvious; use the italian system which was utterly unbreakable (they used 1 time cipher pads which where very popular with the kgb and the nsa in the 70s and 80s and are a huge pain in the ass but totally reliable)
the ironic thing is that italian codes where never broken during the war; and rommel thinking the network was compromised made them switch to enigma
is it a game changer; yes
war winner; no... if anything following some initial german successes it might actually help the allies not to have ultra... they where overly dependent on it and it made them complacent and too conservative in their approach... there where instances where their human intel was better than ultra anyway (and ignored due to their love of ultra) such as the battle of the bulge and market garden