I grow peppers in the greenhouse, and make my own soil mix up. I have on occasion used a cover crop while waiting for the transplants to go in. The results were just ok. The cover crop was quite a pain to manage compared to the benefits I saw. What I do now is to incorporate some undecomposed organic waste into the bed, and let it rot in place. When I plant, the seedlings have lots of rotting compost to nourish them, and the still somewhat undecomposed waste increases the drainage. In beds that are a couple feet deep I might put in 6-8" of material about a foot down. Of course, by the time you plant the seedlings, the bed will have sunk quite a bit. That just leaves room for a top mulch if desired.
Renais

Where in Canada are you? That, like the USA, is a big country with many soil types and weather conditions.
What is fairly readily available in your area, Field
(or Winter or Cereal) Rye, maybe Oats, other grains? Any that will germinate fairly quickly should work quite well. Ordering some from a distant place might mean the seeds do not arrive until long after you want them while locally purchased seed could be sown tomorrow.

I'm currently growing a variety of cover crops in my yard in Los Angeles. It's been in the Fahrenheit 70's (sometimes 80's) during the day and in the 50's or 60's at night.

-Alfalfa is growing slowly, probably because of the cold.

-Winter Rye has grown very quickly and seems happy.

-Common Vetch has also grown very quickly and seems happy.