Will increasing the temperature of my hot water cylinder's thermostat make my shower water supply last noticeably longer?
Absolutely. It will cost you more money to run the hot water heater, but you will have usable hot water for longer. You can calculate the additional time simply as well, it's an algebra mixture problem. I hated algebra, but let's walk through the math anyway:

Let's assume your cold water is at 10°C.
You want the output to be 43°C
Your tank holds 200L.

Given the above, without replenishing the tank, how many L of 43°C water can you get?

 temp = (hl*ht + cl*ct) / (hl + cl)


substitute figures to solve for cl: (200*55)+(cl*10) / (200 + cl)
cl= 72L of cold. 

So 200L+72L = 272L of 43°C before it runs out at 55°C.

Now let's solve for 65°C: (200*65)+(cl*10) / (200 + cl)
cl = 133L of cold. 

So 200L+133L = 333L of 43°C before it runs out at 65°C.

Comparing 333L of hot to 272L of hot, you will get about 20-25% more hot water before it starts cooling. Of course, there's other losses; hot water cool more proportionally before the faucet, the heater looses more waste heat with hotter water, it takes longer to heat water hotter, affecting the recharge rate, etc.

Using an online cost estimator, it looks like you'll spend 33% more money to get 25% more hot water.