Yes. I think people would be less likely to edit pages. To edit, people need to see pages to find something they want to fix. But with hover cards, it discourages people from actually opening full pages.
Let's say that a typical reader (somebody who's never edited before) reads X primary topics in a session. For example, X might equal one and the primary thing the person visited to know about is "Meteorite".
When reading the "Meteorite" article, they see the wikilinks for "bolide" and "Tunguska event", neither of which the reader knows about. Currently, they open those links to find out. Sure, they may just read the first paragraph but they may also likely glance at more and possibly the whole article. With hovercards, you'll get the two sentence'ish blurb about what it is, they'll be satisfied, and move on with reading just the "Meteorite" article. They never glanced at the "bolide" or "Tunguska event" article. So what they never saw was that the "bolide" article contained an obvious grammar mistake and the "Tunguska event" contains obvious vandalism. As fixing vandalism and grammar are both "easy on" ramps to editing, we've missed our chances for this editor to take their first critical steps.
Mathematically let's suppose viewers come to Wikipedia to learn about (on average) X "main" topics and for each main topic they end up via wikilinks fully reading Y "secondary" topics (on average of course). Now let's further suppose while reading any main or secondary topic they read Z tertiary topics (on average). These are topics I'm defining as ones that they only needed the very basics about, like a definition or single sentence description. Without hovercards, the reader would open X + Y + Z articles during their Wikipedia session. With hovercards they would only open X+Y articles (because the hovercards satisfied their curiosity for the tertiary topics). As the tertiary topics will tend to be more obscure and therefore closer to "stub class" articles there will be for them lots of room for non-expert growth because they have lower editorial quality and fewer page watchers for vandalism. So I see readers missing out on Z pages (on average) that were ripe for them to try out their first edit. I suspect that my guess that hovercards could result in a decrease of 10% (or more) in the new editor rate is at the least a plausible hypothesis.
Wish I had more time to elaborate and look up some of the needed statistics. But, unfortunately, I'm very busy with work these days and even finding 30 minutes to edit is difficult at times. I do not have the time to give a researched reply where I find the values for some of these statistics. It's of course possible my intuition is completely off. And maybe there'd be no effect or even the opposite.