Here's the short answer. Yes and no. What - were you expecting something straightforward? This is the '00's people, nothing is simple anymore, just look at the health care crisis. Seriously though, I'll say it once: it is NOT wise to leave the pulp in your juices unless you are buying 100 % organically grown produce that you can verify has NOT ever been touched by the evil Pesticide/Chemical Beast of Doom. Furthermore, if you can't be sure of the "organic-ness", I would suggest you stick to a masticating juicer (one that employs gears) rather than a centrifugal juicer. (Look below the post or click here for some juicer options) You'll understand why in a moment or two.
As I was saying, there's a pretty straightforward reason for this. With normally purchased produce, that is - the stuff that has been chemically treated - you will obviously have these toxins living on your food, raising families, looking for work, having loud parties, and just basically doing what all the cool chemicals do. (Like causing cancer and turning your hair green) These imposing and insidious chemicals will always be prevalent on your produce, and can combine with vitamins and other nutrients as a centrifugal juicer merely chops them all up with the rest of the fruits and veggies. So, yes, they end up in your juice. Conversely, a gear juicer can get rid of most of these offending chemical "squatters" along with the pulp you throw away by combining these toxins with the fibers and pulp. This happens as the foods are crushed and masticated. Sure, some small amounts of nastiness can get left behind, but by throwing your pulp and not ingesting it, you can be assured you're doing the most to keep chemicals away from your digestion and body.
Again, separating the harmful chemicals from your juices is not really possible with a centrifugal juicer, since the mechanics of the juicing process involves merely slicing up the produce, thereby combining the entire produce item(s) into juice. This inevitably allows potentially harmful chemicals to intermingle with everything as it's chopped into tiny bits, and as a result - you may eventually turn a shade of lime green and become radioactive. (I'm kidding!!)
Using juicers that employ gears is definitely a better attempt to separate the harmful man-made toxins - again - simply by the mechanics of how it extracts juice. As opposed to chopping your foods into little bits, masticating gears will actually crush your foods. This allows the healthy nutrients to escape while that lousy chemical crud binds with the fibers and pulp that you eventually toss in the bin.
This may not seem fool proof, and in fact it isn't, but it will be the best bang for your buck if you are concerned about the pesticides and environmental toxins that exist in store bought/treated produce. If you're not concerned about these factors, good on ya. Should you grow toxic and a few extra limbs, I'm sure you can still get work as a superhero villain.
Really folks, as a general rule you should, if at all possible, stick to organically grown produce - stuff that you can verify as authentically organic. Bear in mind why I warn you to verify your produce is organic. The fact is that there are a few - though not many - shady markets that are known for throwing an "Organically Grown" sticker on anything. Believe it or not I have actually seen one on a bag of Doritos once. I'm not kidding.