You can do it. That is what big guys do as well.
First query:
» host google.com
google.com has address 74.125.232.230
google.com has address 74.125.232.231
google.com has address 74.125.232.232
google.com has address 74.125.232.233
google.com has address 74.125.232.238
google.com has address 74.125.232.224
google.com has address 74.125.232.225
google.com has address 74.125.232.226
google.com has address 74.125.232.227
google.com has address 74.125.232.228
google.com has address 74.125.232.229
Next query:
» host google.com
google.com has address 74.125.232.224
google.com has address 74.125.232.225
google.com has address 74.125.232.226
google.com has address 74.125.232.227
google.com has address 74.125.232.228
google.com has address 74.125.232.229
google.com has address 74.125.232.230
google.com has address 74.125.232.231
google.com has address 74.125.232.232
google.com has address 74.125.232.233
google.com has address 74.125.232.238
As you see, the list of IPs rotated around, but the relative order between two IPs stayed the same.
Update: I see several comments bragging about how DNS round-robin is not convenient for fail-over, so here is the summary: DNS is not for fail-over. So it is obviously not good for fail-over. It was never designed to be a solution for fail-over.