This is a pretty obvious SEO question for most of you - but hey - Google's John Mueller confirmed that using the meta noindex tag on your site will not help you save your crawl budget.
Why? Well, think about it. The only way for Google to know there is a noindex tag on the page is to spend their crawl budget crawling the page to find the tag on the page.
The meta tag only prevents the page from being indexed, not crawled. The Google help docs explain:
To prevent most search engine web crawlers from indexing a page on your site, place the following meta tag into the section of your page:
@idanbenor nope.— John ☆.o(≧▽≦)o.☆ (@JohnMu) November 30, 2016
Forum discussion at Twitter.