To the best of my knowledge, no, cookies are not blocked until the user consents.
The plugin allows you to categorize cookies based on their use, and one of the categories is “necessary” – I’m pretty sure these cookies are the ones you identify as being absolutely required to run your website and users cannot opt out of them. They can, however, opt out of the other categories of cookies. But I think even these cookies are detected and used the normal way by default until the user opts out of them.
From what I’ve read, you don’t have to specify to the user the specific types of cookies your site uses, but you do have to generally explain what data of theirs is being collected and how it is being used (including if it is transmitted to a third party, though I don’t believe you’re responsible for controlling how third parties handle that data).
With regards to the forms you mentioned, part of your task is manually detecting which cookies are used on your site, including on all of your forms for whatever plugins you use. So when you find out what cookies Woocommerce, MailChimp, Contact Form 7 etc. use (using the element inspector or a debugging program on each page/window/form your users might encounter), you can specify in the GDPR plugin which category the cookies associated with those forms fit into (“necessary,” “other” etc.).
So when the user accepts/declines/alters their cookies preferences it should automatically apply these changes to your forms as well.
If they disable cookies connected with some of your forms/plugins, it may change their ability to use those forms or plugins, though, so you’ll have to make sure you accurately identify which cookies are “necessary” and place a notice to users that their cookies preferences may affect their ability to use certain parts of your site.