Can I connect TFT LCD screen to Arduino Leonardo same way as it's recommanded for Arduino Uno?
I think it could work, but not easily. I.e. you would need to tweak the code and anyway you will end up with really low performance.

This is the reason:


  SPI: on the ICSP header. These pins support SPI communication using the SPI library. Note that the SPI pins are not connected to any of the digital I/O pins as they are on the Uno, They are only available on the ICSP connector. This means that if you have a shield that uses SPI, but does NOT have a 6-pin ICSP connector that connects to the Leonardo's 6-pin ICSP header, the shield will not work. 


Source: https://www.arduino.cc/en/Main/ArduinoBoardLeonardo


  The screen can be configured for use in two ways. One is to use an Arduino's hardware SPI interface. The other is to declare all the pins manually. There is no difference in the functionality of the screen between the two methods, but using hardware SPI is significantly faster when drawing.
  If you plan on using the SD card on the TFT module, you must use hardware SPI.
  All the examples are written for hardware SPI use. 


Source: https://www.arduino.cc/en/Guide/TFT#toc4

In the end I think it would be better to get the equipment needed...

Edit: You can try with this constructor:


  When not using hardware SPI, you can use any available pins, but you must declare the MOSI and SCLK pins in addition to CD, DC, and RESET.


#define SCLK 4
#define MOSI 5
#define CS   6
#define DC   7
#define RESET 8

TFT myScreen = TFT(CS, DC, MOSI, SCLK, RESET);


Source: https://www.arduino.cc/en/Reference/TFTLibrary