So... you are measuring the time it takes to drain a tank as a function of a specified flow rate (lpm) through the K valve "wide open". This is interesting because last I checked flow rate was dependent on Delta P (Pressure Differential) and flow resistance (head loss)
In fact flow rate = Delta P / Head loss (looks a lot like ohms law)
Sooooo.... your assumption is 100% accurate if you had a constant pressure source (like a compressor) but flawed when you look at the fact that the Delta P is going down as the tank is drained.
You could look at it like you have your stated 1000 lpm when the tank is full but I am thinking you will have 0 lpm when you are at 1ata in the tank. In fact all things being consistant the change in flow rate and pressure will be linear.
Now back to the simplification as stated in a few other posts.
Assume head loss is consistant for the purpose of this discussion.
The flow rate will be proportional to Delta P. So the time it takes to drain a tank is proportional to Delta P and since, as stated in a previous post, the pressure difference in between the tank and its surroundings is less at depth------> the tank will drain slower at depth. Although not significantly so, also as stated in a previous post.