Googlebot will crawl HTTPS links. Source: Will Googlebot crawl HTTPS URLs that are encrypted by SSL?
Googlebot does have a limited crawl budget for every site. The number of pages on a site that Google is willing to crawl is determined by the amount of PageRank in the site and how fast your server is. Googlebot does so much crawling that very few sites have more pages than Googlebot is willing to crawl. Unless you have hundreds of thousands of pages, very little Pagerank, and a slow server; it shouldn't be an issue for you. Google says:
Our goal is to crawl as many pages from your site as we can on each visit without overwhelming your server's bandwidth.
The fact that you use a canonical meta tag means that you will not have any duplicate content problems. Your canonical meta tag will let Google safely identify the duplicate content and tell it which URL to show in the SERPs. Even without the canonical, Googlebot does a fairly good job identifying and correctly handling common causes of duplicate content such as this. Google rarely penalizes for internally duplicated content. For more information see: What is duplicate content and how can I avoid being penalized for it on my site?