I am not trying to avoid hops, but the only recipes that mr. beer uses hops in, its more dry hopping (I think), or boil a few minutes before flameout and extract.
I will probably start with a kit just to get a feel for the hopping and such ..
Probably the first thing you will notice about the recipes you attempt to brew will be whether they use pre-hopped and/or flavored extracts or whether the use the standard unhopped unflavored extract.
The kit that came with your Mr. Beer kit was a pre-hopped flavored extract. In essence you only had to add water and ferment.
Now I'm a bit of a snob. And although we are all friendly to newbies, all the other posters here are snobs too. And in three months *you* will be a snob. And as snobs we tend to look down our noses at these "instant beers" and will thus we'll encourage you to start going into "ingredient kits" in which you utilize your own hops. But all in your own time.
The standard "ingredient" kit will contain several pounds of liquid (LME-- liquid malt extract) and/or dry (DME-- dry malt extract) extract. These extracts will came in a specrtum of light or dark but are a basic standard ingredient (much like flour is a standard ingredient of baking). They have no hop oils in them and are of a standard basic malt flavor with no subtlties.
The kit will contain a small amount of "specialty grains". You can think of these as flavorings. They add color and sense of roasted flavors. You steep them in hot water in a little sock like sack like a tea bag.
And then the kit will contain hops. And, other than sanitation, hops are the only reason you boil your wort. Hops serve basically three functions and ingredient kits will provide up to three sets of hops for these three functions and a recipe will list its hops in three steps for these functions. There are "bittering hops" which you boil for about a full hour. There are "flavoring hops" which you cook for a short time. (Brewers develop their preferences but basically you toss flavoring hops in the last 20 minutes or half hour.) And then there are "aroma hops" which you add in the last ten minutes or so of the boil. The longer you boil hops the bitterer they become. The less you boil hops the stronger and more "upfront" their flavors are.
And that's making wort in a nutshell.
It might seem a bit complicated reading it all without a basic concept of the whole process and abstract and away from a stove but it's actually for logical, systematic and a lot of fun and there's a lot to learn and a lot to enjoy as you learn.
And there's a lot you can learn and fiddle with: Okay, just how bitter you hops will become depends on the alpha acid in that particular harvest and you can tweak it by adjusting the amount of water and extracts you cook it in. But that's a little advanced. Less advanced is adjusting when you add the extract. You can add it all at the start but many folks like to add most of the extract at the end as a "late addition". And that can to a small extent effect how bitter your hops become. There's a lot you can learn but there's also a lot you can take easy at first. It's a load of fun though!
But back to your original question: You'll be just fine doing half a boil and needn't worry about any adverse effects it will have.