The Dink Network

Yep, that'd work

EDIT:
Terribly Late Addition:

While it isn't binary, as other people claim, it is a correct solution. Every bottle will have a unique prisoner-combo, so you can check it that way. Here's the binary way:

The drinks are numbered 1 to 1000, now number them binary from 1 to 1111101000. Those are 10 binary digits. Give drink 1 to prisoner 1. Give drink 2 (binary: 10) to prisoner 2, drink 3 (bin: 11) to 1 and 2, etc. Give drink 1000 to prisoners 10,9,8,7,6 and 4.

When you see dead prisoners, you can calculate the number of the poisoned drink this way:

There are n (say 5) dead prisoners, p_1, p_2, p_3 to p_n (so to p_5 in the example). Say prisoner 1, 4, 5, 9 and 10 are dead, then p_1 = 1, p_2 = 4, p_3 = 5, p_4 = 9 and p_5 = 10.

For every i where 1 <= i <= 10, do this:

d_i = 2^(p_i - 1)

So we get (in our example):

d_1 = 1
d_2 = 8
d_3 = 16
d_4 = 256
d_5 = 512

Add these: Drink 793 is poisoned.