Would a I5 4670k OC to 3.8ghz bottleneck a gtx 770?

Absolutely not.
Also, I recommend the ASUS version or alternatively the Asus R9-280X (The R9-290 is also worth considering but it is $400). The 280X advantage is it has 1GB more memory but thus far it's not been needed. It also allows Mantle but it's hard to say how that will pan out.
http://pcpartpicker.com/part/asus-video-card-gtx770dc2oc2gd5
or
http://pcpartpicker.com/part/asus-video-card-r9280xdc2t3gd5

*Asus GTX770 comes with Watch Dogs
(redeem ASAP, however note it has major stutter unless they've patched the game. They said they were working on it. The video memory fills up quickly then it swaps textures from the drive. Even 3GB cards fill up, or did.)

NVidia's main advantages:
- PhysX on GPU
- G-Sync (new monitors; for smoother gaming)
- Shadowplay (game recording efficiently)
- Steam streaming (via the NVENC hardware encoder that Shadowplay uses.)

PhysX for a few titles that really benefit, and Shadowplay are really what most people care about.

FYI, it makes absolutely no sense to overclock that CPU to 3.8GHz. That is the default TURBO value so you will hit 3.8GHz (if needed) at the default (non-overclocked) settings anyway. Possibly you didn't actually overclock, but anyway the proper "quick" setup is usually to select "XMP" in the BIOS and save. That should also set your DDR3 memory settings to optimal as well.

You should be able on most Z97/Z87 motherboards to overclock much higher depending on cooler but again there's probably not a lot of point to it for gaming.

*Note that you can overclock by a small amount whilst also maintaining the Intel power management settings. If you just click "XMP" it may go higher than 3.8GHz (i.e. 4GHz but depends on the motherboard). Alternatively you can manually change each core multiplier. I got to "42", or 4.2GHz without making other changes.

If I went to 4.3GHz I'd crash my system then I'd have to increase the Intel voltage and make various other settings to be stable but which also significantly increase the temperature (and thus fan noise) so I can't be bothered. On my i7-3770K using Prime95 I went from 68degC to 87degC by going from 4.2GHz to 4.5GHz.

Summary:
- Asus GTX770 + Watch Dogs
- Asus R9-280X (recommend the GTX770)
- Asus R9-290? (recommend Asus OC model, or Sapphire Tri-X and no other)
- "XMP" in BIOS recommended default setting
 
Update:
The Sapphire R9-290 Tri-X at $390 is worth considering:
http://pcpartpicker.com/part/sapphire-video-card-1003622sr

It averages 17% faster than the GTX770 (stock vs stock) and has 4GB of memory. However, since the GTX770 comes with Watch Dogs and costs $310 that's a big difference.

Assuming $40 for Watch Dogs (what it would cost on Steam in several months) we're talking $120 difference.

Other:
*You may also wish to wait a month or so to see if we get better release dates for the high-end NVidia Maxwell cards such a the GTX880. Having said that, the GTX770 is unlikely to drop in price and there's no guarantee a Maxwell card will be a better value.