This would be a very bad idea if the liquid is like water.
Alright, we need to explain a few things here about the difference between straight line acceleration and the kind of agile moves you describe in this question, and how a medium like water reacts in each case. To start with though, we have to explain something else; for all intents and purposes, water is non-compressible.
This is important because it's the rate of change that is going to get you killed in the above scenario. Water is heavy, and non-compressible, just like (say) a baseball bat. You drop a bat on someone's head from a height of around a metre, and they're going to have a sore head. You drop it from 50 metres, or worse, put some force into a downward swing on their head, and you'll kill them.
Now, a bat is solid, water is not. So dropping around 1.5 litres of water (about the same weight as a competition baseball bat) from 50 metres onto someone's head is going to give them a minor headache, but it's mostly going to just make them wet as the water can divert around the head in the atmosphere; a bat can't. In other words, the atmosphere is the MOST compressible element in that scenario, the water next, the head next, and the bat last. That is why you get the effects you do in this scenario.
BUT - Heads are the hardest part of a human body because it is protected by the skull. The torso, where all the internal organs that keep it running are housed, is far more compressible, and in your scenario, you've just taken the air out of the equation completely, making the water and the body, especially the torso, about the same compressibility but your body is now the most deformable element in the scenario, not the water or the ship.
In real terms, what does this mean? Well in the case of straight line acceleration, it means that the body can probably withstand more constant acceleration than it could in an atmosphere. Sure, there is a greater mass pushing on it, but the liquid is probably going to support the body better as the compressibility is similar, especially in the lungs where you would expect the first collapses to occur if you were breathing air scuba style in a liquid environment.
But agile combat moves are going to kill you.
The reason for this is that the rapid changes in direction caused by the moves means that there is a massive amount of energy in play because of the increased mass. The inside of your ship now is far more massive than you are, and it means that doing the same speeds takes far more energy, and the momentum changes are far higher than they are doing the same moves with only a small amount of atmosphere in the ship instead. Every banking turn therefore is throwing huge amounts of mass against you at speed and the impulses alone are going to do you internal damage if not kill you.
The good news is that you're not going to snap your neck because of a sudden turn, the liquid will support you far better than that. The bad news is you won't live long enough to enjoy it as the combat moves will likely liquify your internal organs.
You're actually going the wrong way; since the Apollo missions we've known that filling spaceships with less air is the better way to go. The Apollo ships carried around 0.3 ATM of pure oxygen, allowing astronauts to breathe normally and need less fuel (because they carry less mass), less ship (because the pressure differential with vacuum is smaller meaning you an get away with thinner hulls) and causes less stress on the ship during maneuvers (for all the reasons described above).
On top of that, if you are really talking for military purposes, especially a gunship, you'll find that future space gunships will go into a battle with their crews in spacesuits and NO atmosphere in the ship. Why? Well, first of all a single hull penetration doesn't kill the crew by evacuating the air, and it also means that if the hull IS penetrated, the escaping atmosphere doesn't cause unpredictable velocity changes in the ship by acting as a thruster.
So; if you really want to do liquid breathing, do it in a space suit so that the overall mass is lower and you get at least some of the benefits of liquid body support with far fewer of the drawbacks.