Yes wet braking is a function of tread depth as the void on the pattern helps you evacuate water.
The question is how bad your wet braking distance will be ?
You could see a quick comparison between the wet performances of a 1.6mm tread depth vs full tread depth tires
MICHELIN Primacy 4+ (new : 22,8m - worn : 31,5m) versus BRIDGESTONE TuranzaT005 (new : 22,6m - worn : 36,4m); CONTINENTAL PremiumContact 6 (new :23,1m - worn : 35,3m); GOODYEAR EfficientGrip Performance 2 (new : 23,8m - worn : 35,5m) competitors.
You loose about 10-14m or so. This is a huge difference especially when it comes to an emergency brake situation on wet.
Hence my advice is , please change your tires ! if not please be aware of the risk you are taking.
Thanks. Yours explanation does make sense and quite logical.