Always drain it. The combination of ice/water will make the beer colder sooner, but the water surrounding the ice makes it melt faster for the same reason. Water conducts heat better than air.

But, it is better to have warm beer than no beer at all.

Thanks for your advise and explanation, but it seems such a waste when the thawed ice which is still very cold is allowed to exit without contributing further to the beer cooling effort?

for instance,say the cold water was allowed to cascade over bottles of the amber fluid placed in storage as replacement stock?

I agree It is better to have warm beer than no beer at all.LOL

Agreed that the cold water still has utility for pre-cooling, but if left in contact with the ice, it will such the "cold" right out of it.

Remember, the ice is very likely below 32°F in its interior, but the water will never get colder the 32.

Look, I spent 20 years in the Arizona desert researching this very topic. In every condition imaginable, summer and winter. The combinations I tried are infinite, maybe even legend. This is one topic I know, inside and out.

Now, this all presumes the cooler is in the northern hemisphere. South of the big line, the beer keeps the ice cold.

^{No, wait... that doesn't sound right. Note to self: more research required.}

One thing you could do is put the beer in the cold water and leave it for an hour to let the water absorb some of the heat from the beer. Then empty the water and add the ice. That gives you the benefit of both.

During the hour that you are waiting, have a warm beer so that you better appreciate the cold ones to come.