More fans would result in a cooler system which will reduce the damage heat can cause on electrical components over a period of time. They don't cost that much, so spending some money on more fans will help your more expensive hardware.
Id do it like this.
buy 3 new 120mm fans. scythe gentele typhoons.
Move the rear fan to bottom of case. and put 3 fans rear and top. scythe gentle typhoos is good silent fan and it moves air really even when it rpm is slowed down. buy 1150 or slower rpm fans if you like silent operation.
I like the R4 case but I'm worried if the 2 included fans would be enough to cool them. Is it a good idea to fill the case with 4 more fans?
2 140mm on the front (intake)
1 140mm in side pannel (intake)
2 140mm in top (exhaust)
1 140mm in back (exhaust)
id would fix up the build first
-get the i5 4670k instead of the 3570k
-do not get cheapo liquid cooling. id suggest something like a phanteks tc12dx or a noctua equivalent to provide the silence that comes with the case
-id get the z87x-d3h motherboard with the 4670k. there is a combo deal at newegg
-use a kit of viper 3 red 2x4gb 1600mhz ram. no reason to get 16 when you are only gaming
-id at least get a 760. if you cant, drop the overclocking. always get a powerful GPU and a SSD system before considering overclocking
-a xfx 550w is more than enough to supply the needed power
as for the case itself, there is zero need to put more fans. the entire point of the R4 is to have silence. by putting more fans, you essentailly wasted the case. the hardware you have in the build in the first place doesnt even put out a lot of heat in the first place, the stock fans are more than enough to get them cool