Well, it really depends on your typical listening levels, source material, settings (whether or not the amp will truly output 2000w), other running vehicle accessories, etc etc.
Lets look at this from the "perfect world" viewpoint; If you had a 2000w amp on a constant and stable 14.4V system (which won't happen) and the amplifier was 100% efficient (which ain't gonna happen), at full power it would draw ~139A. That's best case scenario. 80% efficiency on 13.8V would be ~181A of current draw for full output. It takes power to make power, plain and simple.
But, if you aren't going to be pushing the full 2000w very often (due to volume, non-bass heavy source material, lower settings so the amp won't put out full power, etc etc) then the dimming may not be too bad. But, if you expect your amp to output a full 2000w on a stock electrical system; it simply ain't going to happen.
PS: We would need to know a budget before we could suggest amplifiers to you //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif