Please don’t do this:
It will hurt. Not right away, but around sprint 4 when the bugs found in sprint 3 for the stories built in sprint 2 need to be mixed in with the stories planned in sprint 3 for sprint 4. And then it’ll hurt more in sprint 5 and later when you have to start regression testing more and more code each sprint.
Instead, just do as much work as you can get really DONE in each sprint. Plan it, build it, test it, and deliver it. It’ll be hard to ensure that testing doesn’t get squeezed out the back of the sprint. It will. When that happens, try moving testing to the front of each story. Create your test cases as specifications and then do just enough development to make them pass. (Consider a tool like Cucumber for this, using it to drive Watir if you’re building a web app. Or look at Fit/Fitnesse if that’s more your style.)