Do you need initialization when sending raw RGB data to a ILI9341 based LCD?
Well, you can always send RGB data to the ILI9341. In the end, it just has a block of graphics ram that you can read and write from using the memory commands. I guess the real question is whether that data will appear in any sort of useful way on whatever LCD panel the ILI9341 is driving.

The answer to that is it will not unless you perform at least a basic level of initialisation. At a minimum you will need to issue the 0x29 display on command. That might cause something to appear. But to ensure the display is being driven properly, you need to setup the power settings for the controller. There are a number of these commands and they determine the voltages sent to the panel to control each pixel. If these are not setup correctly the panel will have poor contrast and colour representation, may not work at all, or could even be damaged. You will probably also want to set the graphics ram to screen pixel mappings, and maybe even the interface/colour format if the default settings are not suitable.

Any decent LCD supplier will include a basic list of initialisation commands to suit their particular panel. Unfortunately there are no shortcut to this, and you'll either need to talk to the module supplier or, at a minimum, copy the initialisation code from a similar product.