Unknown, since everybody thinks different things sound "good". But generally, cheap headphones are cheap because they use low quality components. To make up for large diameter drivers, they make them low impedance which drives them harder, etc.
An amp, won't do anything other than OVERDRIVE cheap headphones. That won't improve them.
A DAC and Amp will offer a higher quality source to any headphones and potentially drive them better.
The question is will cheap headphones benefit enough to make that improvement greater than getting better headphones?
It makes more sense to me to go for better headphones first. You don't know which amp will match best with headphones you don't have yet.
If your source is of sufficient quality, then a AMP/DAC combo could improve the quality of your headphones. The placebo effect will probably make you think it's better, however in reality it's probably just louder.
For high-end headphones a AMP/DAC will make a world of difference since they have the fidelity to bring everything up. Lower quality headphones won't benefit as much since they won't be able to really bring up the details.
Now then... As for what goes for EQ's. It might make them better. Again, it's up to the individual to decide what sounds good. Personally I really like my sound signature to be flat, hence why I got the HD800's and I wouldn't change a thing about them. If you feel like there's a lack in the highs then go ahead and add some. If you feel like it's better then it is.