Is it a good idea to try and make my readers feel attached to the character's home in order to increase the emotion of the moment?
This depends on the story. Why do you want to increase the emotion of this moment? Are these emotions something important to the story, something that drives the plot forward or deepens the character? If so, then it is absolutely a good idea to include them. Finding out why you want to include something can often tell you if you should.
EDIT: Upon rereading your first question, I realize you may be asking if making your readers feel attached to the house is a good way to increase the emotion of the moment. My answer is that it certainly can be, if done right. See the below to see what I mean. Getting the reader attached to things is the whole idea behind stakes, something every novel needs.
Is spending a little more time describing the character's home and its surroundings a good way to accomplish this?
Once again, it depends. I think Fell has a great point in his answer, which I will quote here for convenience:
This doesn't necessarily mean you have to describe the color of the paint or the type of moulding. On the other hand, worn carpeting that indicates well-trodden paths from point A to point B can speak volumes about the character and his/her place in the home.
That is a great example of using the physical house to describe the emotions of the character. Remember, your goal when your character leaves his home is to increase the emotion of the moment. Simply describing the house isn't going to do that, especially not in a short time. Describing how the character feels about the house, though, is completely different. You can easily describe specific objects that evoke memories in the character, for example.
Focus on the emotional, not the physical.