I've played with this question a bit and the answer is definitely yes for CRC-32-###. Which does not require brute force methods. So, you can make a fast self refencing string, if you know the magic incantations and a few tricks.

the cRC of THiS StRinG IS OBviouslY 0XBEefc0de.

If the trick isn't obvious here you can toggle case to adjust the CRC of a string, without changing the meaning.

But of course, you need to know which bits need to be toggled. And here linear algebra is your friend. because CRC is linear... it means at least for this problem. If you toggle a bit in the string the output crc will have a set of toggles associated with that toggle. So once you have 32 things you can toggle you can make a 32x32 matrix and solve for a set of toggles which have the properties you want.

thE aNsWEr To LIFE thE UNIVERse aNd eVERYthing is actually 0x42!

I used a simple thing that just tries different combinations of caps. But it is kind of obvious? isn't it?