Not really. You have better luck with whatever document you have to prove your U.S. citizenship for your EDL application than a DMV letter.

While Canadian law does not strictly require U.S. citizens to have a passport to enter the country, the border officer has the power to deny you entry if they are unsatisfied by your identity and citizenship. Only a passport (booklet or card), NEXUS/FAST card or an EDL constitute a definite proof of U.S. citizenship for Canadian authorities. Whether the border officer accepts other documents depends essentially on their mood.

If you do not carry proofs of citizenship and identity, you may also face difficulties when trying to renter the U.S. You are most probably still be allowed to enter the U.S., but you may spend some time (even hours) while CBP verifies your identity.

Not really. You'll have better luck with whatever document you have to prove your U.S. citizenship for your EDL application than a DMV letter.

While Canadian law does not strictly require U.S. citizens to have a passport to enter the country, the border officer has the power to deny you entry if they are unsatisfied by your identity and citizenship. Only a passport (booklet or card), NEXUS/FAST card or an EDL constitute a definite proof of U.S. citizenship for Canadian authorities. Whether the border officer accepts other documents depends essentially on their mood.

If you do not carry proof of citizenship and identity, you may also face difficulties when trying to re-enter the U.S. You will most probably still be allowed to enter the U.S., but you may spend some time (even hours) while CBP verifies your identity.