We recently were asked the following question on a Data protection forum:
“There is a website called specialneedsuk.org which publishes 100s of email addresses for special need schools. As I understand it GDPR prohibits us from sending them an email with a discount code for goods relevant to their institution.
Would it be allowed to contact them asking whether they would be interest in receiving information about our company without offering the actual offer?”
Any promotion of your business by email, telephone or SMS, whether it is directly, or asking if they'd like information is marketing under the Privacy & Electronic Communications Regulations.
It cannot be assumed that the email addresses are generic mailboxes, they may be manned by only one person, in which case they are that person's personal data, so in our professional opinion, it would be dangerous to use it in the way you suggest.
We have previously wrote an article about ‘When is it OK to use “publicly available” data? which you can read here.