Need confirmation if this 2 new components fits

[Gacsoka]

Hi there Everybody, I need some help to confirm, if my upgrades will start my PC without blowing it up. I'm really new to it, but I've seen a lot of reviews, so I chose this card and power supply.
So, right now, I have:

AMD Athlon II X4 641 [PICTURE] OC->4GHz ( I might need to turn it down from 4GHz, but since summer, it's working beautifully. )
F1A55-M LX Mainboard
1x4 GB DDR3 RAM
An AMD Radeon HD 6670 1GB
Kolink CHS 450 - 450W PSU


Now, I would like to upgrade my GPU and my PSU to
-> PCI-E HD7870 2GB GDDR5 PCI-E 2XDVI HDMI DP GHZ EDIT [222$]
-> Corsair CX600 Modular [84$]

I would use this for PC gaming.
I checked, and both can fit in my Case and my Motherboard can handle the HD7870
Now, the question is:
Is my CPU enough for this card?
Is this PSU is enough for powering all this?
and at last, Is it worth it?

I'm open for any more suggestions, maybe for these two components, or something for the future. I have only 360$ to spend right now, and the next upgrade will be my CPU. ( Maybe next year. )

Thank you for reading.

 

[tiny voices]

Your CPU should be ok. It may bottleneck in CPU intensive games a bit like BF4.

The PSU is more than enough.

 

[Gacsoka]

Thank you for your quick response!
I know it will struggle a bit, but I hope it will be fine until I can get a new CPU.

 

[tiny voices]

It will be fine until you upgrade it. Always glad to help!