No, you probably shouldn’t. I’m guilty of over-checking. I was thinking about this recently and decided I’d give myself a few times a day to check and then move on to actual productive work the rest of the time.
One of the problems of checking (and then in my case replying, because I hate having email sitting around) is that it gives people the idea that they should expect you to respond so quickly. You’re training them that way and it just gets… annoying, I guess? Then if, god forbid, you have to put off replying it seems like you’re “not responsive”. It’s not a good cycle.