I'm a senior in mechanical engineering and am a proud member of my sorority!!! I'm SO excited that you are thinking about going through rush!
I'm assuming you are a female, so I apologize in advance if you are a guy!
Firstly, I want you to stick with engineering!! Don't let anything- or anyone- discourge you! You will be putting in more work than your peers. You will also meet lots of people (especially in greek life, at my school) who have majors that don't require as much work. At times you will feel that life is unfair because other people don't have as much homework as you do! But don't worry- you'll get through it!
Secondly, my number 1 reason for joining a sorority was that women are hard to come by in engineering. Sure, you will have girls as roommates, but as life (in engineering) goes on, you will be spending more and more time with guys on group projects, study groups, and in class. When my boyfriend (also an engr major) suddenly broke up with my in sophomore year, I realized I had no girlfriends to go crying to!!! That's when I knew I had to rush.
I am very involved in the Society of Women Engineers (on a local and national level) but still, I am lucky if I have another SWE member in my classes! I def!! encourage getting involved with SWE, but they are generally more of a pre-professional organization than a 'friendship' organization.
I am the only engineering major in my chapter of about 140 girls. I have a small officer position. Being in a difficult major, and in a GLO, is a huge time balance. You need to work out a schedule and stick to it (i.e., you have to learn to NOT play on the internet for the 3 hrs you have between classes, but to do homework instead). That way, you will have time for your GLO's activities in the after hours. Going out, socials, and late night activities were always hard for me since most engineering classes are either early in the morning (7:30 AM) or late at night (6 PM or later) to cater to those of us who do internships and co-ops. Unfortunately, that usually doesn't change and it's hard to get around it. I've had to say no to going to socials that lasted until 2 AM (although I WOULD go if they came back at midnight or so).
It is definitely feasible, but you need to remember that you are in a much more demanding (not necessarily more difficult) major than your peers. ALL of your five (or however many) classes will require you to do lots of really hard homework !
There's no way you can slack off, even on one homework, and pass the class- at least at my university. There will be lots of fun, smaller, bonding activities such as banner painting, buying decorations for skits, etc that you will have to pass on.
But- never forget your sisterhood. You will need to make sacrifices so that you CAN bond with your sisters. I have seen too many (okay, only 4) girls that are engineering majors in sororities that have pretty much abandoned their sisters in the name of academics. Don't forget that college is about having fun too! If you have any more Q's feel free to PM me, or I can continue answering them here for the benefit of others with the same question!