Yes, more than an "ice-breaker", having a drink and conversation start the engine up.

to be offered a drink when I arrived.

 
If a gal comes to my place, I am always sure to offer one.

 
It's a practice I would love to see revived.

I always ask ahead of time what they might like to drink. If it is in the morning, the answer tends to be a morning non alcoholic beverage. Afternoon or evening it tends to be alcoholic. I bring or have on hand what ever they prefer. Being 250 years old, I find the conversational time and important part of the companionship.

Yes, and perhaps sushi? With the right person.

I love starting the date with a smooth drink! Particularly love a hand crafted limoncello over ice during the summer.