Most email marketing platforms support batch or staggered email sending so you do not blast all of your email list at the same time and then spike site traffic for all customers trying to access a deal or a product page at the same time.
If you have a CDN setup for your site make sure that assets and static HTML page rules or even caching rules are in place to cache as much of those landing pages or product pages as possible to be able to deal with increased traffic. Using a CDN such as Cloudflare will help keep PHP-FPM worker usage down by having edge caching in place.