It is unlikely that all users who sign up to try out your product are going to activate their accounts to the same level. Some users might require a push or a nudge to activate their accounts.
Sending emails to the user over the lifetime of their trial based on their activation and usage pattern can be a great way to engage users who have not completely activated their accounts. GrexIt nudges its users upto 4 times over the one month trial period to start using their accounts actively. Brightpod has around 6 emails that sent over the 14day trial. The automated emails that are sent out contain context about the user's usage, and tell them the next steps to take to further activate their accounts.
Lifecyle emails for activation can be implemented very well with tools like customer.io or intercom.io.
There will be users who would never activate their accounts. There also will be users who activate but never buy. Your goal is to keep them engaged to your brand and product. One way to do this is to add them to the list of users to whom you send content from your blog. If you are posting content on your blog that has insights about your industry, and is useful to your audience, your subscribers would love it, and would be reminded of your company every time they receive a new update from you.