Nope. An e-bike is merely restricted to 20 mph on flat ground when the only propulsion is the motor. Add in the human engine, and one can go much faster than 20 mph legally. In fact, this is what I would recommend for the OP. Sure, even at just better than 30 mph, achievable with the e-bikes currently on offer at either Wheelworks or Arriving by Bike in Eugene, it's a two-hour each way commute. However, that's two hours of riding versus one and one-half hours of lost time behind the wheel of a car. Four hours per day on the bike, even with electric assist, will keep/improve your fitness.

I spent a number of years commuting into Eugene from the opposite side. My commute was 45 miles inbound and 65 miles home (traffic conditions dictated taking the long way home). Did I follow my own advice and get an e-bike? No, I just rode my regular old pedal bike, but I sure was fit.