Will the card fit?

Solution
No way it will fit , very tight inside.
311.91mm is the length of the card
Maximum Supported Video Card Length 210mm 🙁
[video="https://www.youtube.com/watch?v=9JzTSo2wqQc"][/video]
My guess would be no. Looks like a motherboard would barely fit and that GPU sticks well past a standard atx board. You might be able to jostle it in there though, power connections might be problematic.

Certainly wouldn't use the included PSU for it.
 
No it won't sadly, I checked the measurements and the case supports GPUs that are up to 210mm long which is 21cm. But the GTX 970 is 31.2 x 12.9 x 4.3 cm so it is too long to fit.

Also I really wouldn't recommend that PSU, like Eximo says it looks awful and is quite small for a GTX 970.

I would buy an EVGA or Corsair PSU like:

Corsair RM750
Corsair CX700M or CX600M
EVGA Supernova 650W