The short answer would be "No."
But, if you are willing to put a decent chunk of effort into it, it could theoretically be done.
A couple of the steps that you could take in order to get as close to your desired result as possible would maybe be some one the following:
From "Home", find the Groups section on the left, and click it. Followed by the word Groups at the top left. (It shouldn't be styled differently, but if it is for some reason, it wont be hard to find the button on either page.
Once there, you may select the group you want, and change the notification settings to ALL which would give you both types of notifications. You'd leave it that way until a few steps further.
Next, go to the actual page, and make sure the settings (listed near the top of the page - likely within a drop-down menu) correspond with your preferences.
Then when that's done, go to your main Settings page which is the one on the upper right, by your avatar. Once you are there, play around a little bit with the settings, but the main things you're going to want are in relation to email alerts and notifications..notifications will be limited on what can change but email is almost completely open.
Once you change your email settings to one that will accept all or most emails (whichever one will give you the group emails you're looking for) then try to make some changes to the other notifications if possible. If not, exit back to the home page.
From Home you will likely have to wait until you get a notification about the group, but when you do, if you pull the notifications down, you may or may not see the option (for the group notification, when you hover over it in your notifications alerts) to do several things which very likely include different types of notification settings based on the person, or the group. Change them to your preference.
Depending on what your email provider is (I have Gmail) you may go to the Email account and make some specific changes regarding which emails you are going to accept from Facebook...I personally gave Facebook its own folder and set a rule in the inbox to direct ALL Facebook traffic there (which you may do via keyword rule, senders address rule, etc)
Sooner or later, you will accumulate emails from Facebook regarding different things. The goal here is to determine which can be deleted or diverted, and which ones you need to keep track of...and quite honestly, the best way to do that would be the following:
Make sure you have an email about a comment made in your group. This will come in handy when setting the rule up in your mailbox.
Once you've got that, obtain a few other emails that are not related to the group or comments in the group. The reason for this is because you are going to want to compare the emails and create a rule that will divert ALL emails that are not specifically regarding both that specific group and a comment placed in the group on a post.
For example - an email about someone commenting on your status, has nothing to do with the group. If you can determine a phrase or series of words that is being used in those types of emails, that is not in any of the emails you get for group notifications - you can set a rule to trash all emails that include that phrase. Of course, you could do it completely the other way as well. Whichever is easiest on you.
Basically, you're going to just manually make sure that FB doesn't send you the emails that are not about the group - but that the group messages do arrive for you.
You can go a couple steps further and only accept the ones regarding comments - in which case you would just do all the previous steps, but then once you're already getting ONLY group emails - take the emails regarding "Posts and those regarding "Comments" and find out if there is anything different about the two (like you did with the Group and the regular ones) and narrow it down even further by sending all the emails regarding posts to your trash and keeping only verrry specific emails - those that tell you about someone who is commenting on a post - and not about the actual posts themselves!
I'm not sure if you're willing to do something that odd - but it will work, and you will get almost exactly what you are requesting. It's not simple, but its the only way to do it pretty much. The feature you are asking about does not exist, therefore it needs to be manufactured in one way or another. Although difficult, this seems to be the easiest way!
