Their marketing is quite aggressive (I have been receiving "Last month to get Linkedin Premium for free" weekly for about an year!) but I wouldn't call them spammers.
What you describe I would describe as spam. Obviously there are wildly different informal definitions of "spam" in use. By my definition, Linkedin is definitely a spammer; I get frequent email from them and I don't have, and plan to never, get an account.
They seem to continuously invent new things to mail you about, as often as possible, which you then continuously have to uncheck on the site.
We can argue about definitions but in my mind LinkedIn are definitely spammers, that are now only tolerated because the site is too popular for jobs (especially if you're a contractor).
They didn't use to be like this, but they now have the questionable distinction of being the nr.1. deliverer of junk in my mailbox.
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