Rails 4.1: Asset Host via Amazon CloudFront in context of Slug Compiler error

With my current master branch, I have too many image assets that do not allow me to successfully push to heroku without getting a Slug Compiler error.

If I change my content delivery of assets to Amazon CloudFront, will that allow me to somehow circumnavigate this error? Will it automatically push my assets only to my cloudfront distribution as soon as I change the following line:

config.action_controller.asset_host = "<YOUR DISTRIBUTION SUBDOMAIN>.cloudfront.net"

I am confused about how the assets, which are currently in version control, can be distributed via a CDN without me doing a git push heroku master which currently gives the slug error and hence my problems are triangulated.

I suppose that if I remove all assets from git and use an FTP service to add to them to my AWS Distrubution subdomain, then any =image_tag will function as always and I will avoid getting my current Slug Compiler Error?