How you spend the money may make a $2,000 budget sound better than a $4,000 budget; for example, a person may insist that all five speakers must be the same (which is fine if the budget allows it), but that would require a cheaper choice in speaker than if they had went with inexpensive surround speakers, and put the saved money to better mains and/or subwoofer (honestly, how often does a person critically listen to surround effects?), or if you like to watch movies at reference level, then maybe spending a bit less on a receiver and putting more money toward a power amp would make things sound better.
And if no attention is given to room acoustics (i.e. room treatments, subwoofer EQ and/or multiple well placed subwoofers), your movie watching experience will be less than it could be.
As for being happy with a $2,000 system; if you addition some 2k and 4k systems, and find that 4k doesn't sound all that much better than 2k, then yes, you can be happy by spending 'only' two grand.