Why, yes, it's eminently doable. Even a single byte will let you discard 255 out of 256 attempts, and as you kindly point out, 4 bytes would be enough to uniquely identify almost any word in the standard dictionary.
Feel free to peruse some SHA-256 hashes with slightly above six bytes of fixed prefix - several orders of magnitude more difficult to find than a mere 32 bits partial collision: http://blockexplorer.com/
Now you can argue about how likely it is for an attacker to actually bother to find and exploit such a weakness, and how a salt would mitigate the severity and so forth, but the takeaway here is that this attack can be trivially and permanently defeated by using a timing independent comparison function.
Feel free to peruse some SHA-256 hashes with slightly above six bytes of fixed prefix - several orders of magnitude more difficult to find than a mere 32 bits partial collision: http://blockexplorer.com/
Now you can argue about how likely it is for an attacker to actually bother to find and exploit such a weakness, and how a salt would mitigate the severity and so forth, but the takeaway here is that this attack can be trivially and permanently defeated by using a timing independent comparison function.