I’m afraid that won’t be possible, as you can’t import subscribers from a third-party plugin into Jetpack.
You could, however, use Jetpack’s Subscription form shortcode to display a subscription form anywhere on your site, including in a pop-up for example, and thus collect Jetpack Subscribers directly.
To add shortcodes to pop-up modals, you could use a plugin like this one:
https://wordpress.org/plugins/popup-builder/
Can we expect this importing feature in the future?
We’ve talked about it, but haven’t found a good way to import subscriber lists without hurting the quality of our service yet. You can follow our discussion here:
https://github.com/Automattic/jetpack/issues/535
I see some email providers in internet claiming that, if the email bounces, then they will remove it from the list.
Can these features avoid getting WordPress.com spam ? ( Provided Jetpack allows importing emails)
That’s one way to clean up lists, but that doesn’t protect against spammers adding legitimate addresses to a giant subscriber list against their will.
We’ve talked about other options though, and we’ll definitely consider adding an import feature if we ever find a good solution to this problem.