Yes you can get by with the stock Intel for a short while as long as you do not overclock or run any stress or stability test. I would never run such an expensive and high end proc like the i7 4790k on the stock Intel cooler unless I wasn't doing anything more taxing than general use (which would be silly with a 4790k). That stock cooler is adequate, and thats all. Well actually its barely adequate.
I understand money issues, but you really need a good after market cooler on such a fine processor. It is after all still a Haswell, and is going to run warm when you push it. That cheapo Intel stock cooler can't handle any real cooling duties- just basic cooling with no stress.
Try for a closed loop liquid cooler (don't know what case you have), Corsair H80i, H100, NXZT etc.... if possible, but yes the Hyper 212 EVO will also be fine for the less expensive choice.
By the way, I quit running Prime95 or Intel Burn test on my i7 4790k. I know my proc is stable and rock solid at this point, and those benches just put unrealistic loads, and too much stress on the DC proc. Haswell can't take it. I initially ran Prime95 on my 4790k and stayed in the high 60's (C) but then realized I had Hyperthreading off, AVX off, and manually set voltage low, which kept my temps unusually low. I only fooled myself because when I set voltage to auto and turned those two functions on, temps soared toward 90 (C). Try running Aida64 is you need a stability test.
DC procs just can't handle Prime like SB (or even IB) could. They will freaking burn up. Still a great processor though and so fast it just plain crazy. I think its safe to say at this point its just not the OC king that Intel led us to believe it would be. I'm very happy with mine though, and I keep it running at 4.4Ghz 24/7 with my MSI mobo's "Enhanced Turbo" function. No temp problems at all there, and I idle in the mid 20's (C). Under load (gaming, etc, NOT PRIME), it runs in the mid 40s (C). Aida64 stability test runs in the mid 60s (C).
The 4790k is a fantastic proc, get a good cooler man. Please.
Good:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835103099
Better:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835181031&cm_re=h80i_corsair-_-35-181-031-_-Product
Best:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835181032&cm_re=h100i-_-35-181-032-_-Product
Best #2:
http://www.newegg.com/Product/Product.aspx?Item=N82E16835146042