Nope. First step to FI is eliminating debt (mortgage usually excluded since you often can beat the interest rate with investment return, and everyone needs a place to live). An electric bike is a luxury, not a need. Wait until you can afford it.
Regarding the, "Is it prudent since we'll potentially be saving money in the long run?" the answer is still no. A regular bike is a practical alternative. Any time a decision needs to be made, analyzing what better alternatives are available is a must.
Good luck on your journey!