I am currently part-time and my school provides most meetings for associations, etc. after 5pm and before our evening classes start. I'm not sure if any other schools do, but ours does. Most part-timers have jobs and are going at night to lessen the burden of the debt - at least that is what I'm doing. I was told that moot court and law review are definitely doable for part-timers and the current editor of our law review is a part-timer, but externships are not. They were fairly honest about this up front.
I think it really depends upon the person. Although I won't be able to do an externship, I have been invited to intern with the legal department at my current job when the time comes. In addition, I work at a private club and already have a network of numerous attorneys - many more than most of the full-time day students. All are aware I'm in law school, many I've known for years, and one who says there will be a job waiting for me when I graduate. Of course nothing is a guarantee.
The upside is this - you have work experience and less debt. It's not legal experience, but if you work in the business world, you have knowledge of business in addition to your legal knowledge when applying for a corporate legal job. Same if you work for an insurance co., etc. I will not be graduating with over 150K in loans desperate to take any job anywhere. I can slowly start a solo practice if there are no opportunities. But, as the old saying goes, "it's easier to find a job when you have a job." It will only take me one year more to finish and I'll have about 1/3 of the debt. Moot court, law review, externships, they are all important when finding your first job. However, most of the attorneys I know have also said that once you move on to your second or third job, those things don't matter as much if at all.
Another judge I spoke to went part-time at night while working full-time and was able to do moot court. She didn't find a job right out of law school, but was hired with the public defender's office within a year. She made contacts doing unpaid interships while working solo after law school. She had do a bit more, but now she's a judge. Perserverance is key in any profession. Remember, you can't send out only 20 resumes within a two month span and whine that no one gave you an interview. It's really not impossible, but it will be a little more work and a bit more sacrifice to get there.