We have done several battles of 2,000 points+ per side.
While they do take longer than a 500 point battle, it is not a proportional increase.
Our last 2500 point game took about 3 1/2 hours and was Klingons versus Kzinti.
At Nashcon, we did a 4,500 point a side battle. (roughly 30 ships a side)
Even teaching new players, we played 5 complete turns in less than 8 hours - and much of the time was actually spent looking for the correct record locarion to record damage than actually playing the game.
so yes, ships do blow up faster.
As for init sinking... it really doesn't change things.
If you run squadrons and your opponent doesn't, your opponent has the initiative advantage... but you're going to be blowing his ships up faster than he is yours and many of his will die before they get to fire. Then, the intiative sink advantage will not matter.