This is one of the most fiercely debated topics on the forum. I believe it's safe to say that EMT experience will teach you next to nothing medically, however, the experience you gain in EMT fundamentals will come in very handy when you're doing your first clinical ride outs on an ambulance.
Knowing how to operate the stretcher, find things in the ambulance, take a blood pressure while you're moving, get paperwork signed, all of the little things that you learn as an EMT will become ingrained, allowing you to focus on the ALS interventions and the clinical presentation that you're being graded on as a paramedic student.
So, should you work as an EMT before becoming a paramedic? That ultimately it's up to you and your paramedic program's requirements. Many successful paramedics had zero experience when they entered the basic class. But, most paramedic students with no EMS experience might tell you that it was a longer ramp up. Every preceptor I've met who has to teach BLS along with ALS finds it takes more time to get providers comfortable.
But hey, everybody's different, and I'm sure the next post will present a totally different viewpoint.