The 750DJ have a listed impedance of 32 ohms. Sure. A headphone amp alone could improve the SQ. Particularly if you like bass. A headphone amp may bring out the bass impact more at higher volumes where the weak output of the built-in amp can't keep up on bass heavy music like EDM, hip hip, etc.
And I agree. The DAC implementation in many laptops is typically not very good and a DAC could improve on clarity and detail.
If you want to stay within your budget, then the FiiO E17
could be a good choice, a portable USB DAC/amp. Here is the discussion thread for it: http://www.head-fi.org/t/587912/fiio-e17-alpen-first-impression-final-thought