No
You can send an email to 1000 different users. A lot of companies send millions of emails per month !
It first depends on your users
Users can mark the email as spam if you send it without their mutual consent or send 1000 mails to each, obviously !
But in your question you explain that your users have given their consent because they are subscribed to your mailing list, so thats good.
Secondly it depends on your mail content
It depends mainly on your mail content.
There are a plenty of different reasons that your content can be marked as spam.
- some word in subject
- the ratio text/image of your content (too much images can be consider as spam by mail client)
There are a lot of words which can marked your mail as spam by the mail client.
a non exhaustive words list : https://blog.hubspot.com/blog/tabid/6307/bid/30684/the-ultimate-list-of-email-spam-trigger-words.aspx
In a lot of cases, emailing services can be very useful
You can use service like MailChimp or SendGrid to send huge amount of emails. They have free tier plan to try their service.
e.g with SendGrid
Send up to 40,000 emails for the first 30 days and 100 emails per day free forever
with MailChimp
Forever Free
Up to 2,000 subscribers and 12,000 emails per month
Moreover they have a nicely done dashboard with a lot of information about your sent emails (spam report, devices, clicked mails, opened mails etc..)
Last recommendation
You can use a service different for your marketing mails and your transactional emails. So marketing emails don't impact the reputation of your transactional emails (they are more important than marketing mails)