Can I calculate (approximately) how much air pressure is lost by measuring the hose length and diameter?
No, you cannot tell how much pressure is lost based on the size of the hose. This is not because there is not enough information to tell but because the hose is irrelevant.
You seem to be under the impression that there is some total amount of pressure in the hose and in the inner tube, and when you disconnect the pump and release the pressure in the hose, some of it is lost.
This is an incorrect understanding of what pressure means. Pressure is an intensive property — it is something that is the same for of all the air no matter how you divide it up within the connected system. The pressure in the hose equals the pressure in the inner tube, which equals the pressure in the whole pump-and-hose-and-inner-tube system.
In the tradition of physics education, let's consider the ideal case with a separately controllable valve on the tube. This is what would happen:
With the pump attached to the inner tube, you open the valve. This causes the pressure in the hose and tube to equalize: this is when the gauge on your pump jumps upward. At this point, the pressure in the tube has reduced, because some of the mass of air in it moved into the hose to pressurize it.
You use the pump to increase the pressure as desired, according to the gauge.
You close the valve on the tube. The pressures on each side of the valve remain equal to each other and to that read by the pump's gauge.
You disconnect the hose. The extra air in the hose escapes to the atmosphere.
As soon as you closed the valve, the inner tube became a closed system: the pressure in it is no longer affected by anything about the pump. It will stay where the gauge said it was while you were pumping.
Now, in a real valve and pump chuck, there isn't a separate control to close the valve (pumps may have moving center pins to push the valve open as part of the “lock” but they aren't always exactly the right length — but I've never used a Presta valve so I may not have this right for those), and it is instead closed as you pull the chuck off the valve. This may release some air from the tube, due to the valve not being fully closed before the connection starts being open to the atmosphere. However, the amount of air released from the tube depends on the valve and how fast you let it close. It does not depend on the volume of air in the hose (except insofar as the pressure in the hose opposes the pressure of the tube even though both are also flowing out to the atmosphere, which is probably a minor effect).