To be honest - I don't know about the possible effects.
So everything that follows is not backed by any study or hard data, just my 2 cents:
I would guess google takes a combination approach. A website that has no links, bad user interaction and only direct traffic (= from mail links) will probably be rather seen as spammy than quality website, on the other hand a website with an already good standing might profit from email marketing, because it might be a signal for google that there is a real business behind a site.
From my point of view there is more to it though:
With gmail google is running one of the largest email providers, so they know not only that a link in a lot of emails came to the surface (no matter whether html or plain text), but they also know whether it is a one time burst, or a consistent email campaign, and they also know whether people move that mail into their spam folders or not. A link that turns up mostly in emails that people consider spam will probably hurt a site whereas links in emails that get read a lot might help.
But don't forget - this is all speculation - it might very well be that google is not even allowed to analyze email content in such a way (at least in Europe).
They might do it nevertheless or they might not - I just don't know...