I'm not sure what you mean by "reply about the medical". According to the website / staff instruction you seem to need the medical in hand to fill out the application. It may work with just the file number - I don't know for sure.

Conversion agreement between U.S. and Canadian officials - Transport Canada

I did my conversion exam in Winnipeg. They were accessible, informed, and friendly. Recommended. Indeed, you could Skype their office and ask them your question directly.

Oh. yeah, I didn't have to leave them my logbooks. They had a look and handed them back to me when they were satisfied. There's 20k + hours of flying (a lot of books!) so they didn't feel the need to keep 'em, I guess.