Sorry to disappoint you Rob but the "Intel HD graphics" is actually being delivered by your i3 processor - you don't have a separate card. As previously stated, it's highly unlikely you'll be able to upgrade the graphics. Even if it were possible, Photoshop and Illustrator are applications that mainly utilise CPU and RAM for performance not the graphics chip.
Would increasing the RAM from 4 to 8GB increase the graphics performance significantly?
Possibly - although 4GB is usually more than enough for most users. If you're working with ultra-high resolution images in Photoshop then a RAM upgrade may help. You can test for this yourself by opening up all the applications you'd normally have open at the same time then checking how much physical memory is free by going to Task Manager -> "Performance" tab and checking the "Memory" bar graph on the left-hand side. If there's 1GB or less of available memory then it's likely you'll benefit from an upgrade.
As I have done it,I have proof that it works, so I know it works. It works better than adding Ram. Only way you get any benefit from extra Ram is if you do lots of intensive tasks like Video editing and in that a Faster drive will be just as much good