It depends on the skill in question.
First off, channeled skills are exactly the same as normal skills in terms of triggering things, except you do not need to re-cast the ability between each tick. Each channeled skill has a "Tick" (that occurs more often the faster attack speed you have), and it is these ticks that trigger on-hit effects. Each "Tick" is when you pay the resource cost of the skill.
Now, whether channeled skills are better depends on the on-hit effect you're trying to use. Anything with a listed % chance on hit, e.g. 1.1% chance to fear on hit, will be better the more attacks/ticks you make. Something listed as a "chance to happen", such as the wizard's "Critical Mass" i. e., "Critical Hits have a chance to reduce the cooldown of your spells by 1 second. " are most likely set up for ppm (proc per minute), which means you have a better chance of triggering them with a slow weapon, with the intent that you get the same number of triggerings, procs, over any given time period as a faster weapon.
Lastly, bear in mind that all that matters is the "Tick" times. If Rapid Fire shoots 10 arrows per Tick, all 10 of those arrows represent a single chance on hit (much like the Monk's Way of a Hundred Fists)
So to conclude, no, it is not better to use lots of channeled / DoT skills, for the simple reason that they don't provide any innate advantage. Unless you're fishing for Procs, you'll gain a much better chance to trigger things by using a faster weapon than any particular ability.
Best Answer
To calculate this, we need to know about a certain skill property that is commonly known as "Proc coefficient".
Each skill has this coefficient, which is a percentage between 0 and 100%. A value of 100% means, that on hit efffects (like stun on hit, freeze on hit, life on hit, etc) happen (proc) on each hit with full effectiveness / chance. So if you have a freeze chance of 3% and gain 10k life on hit, with a proc coefficient of 100% you will gain the full 10k life per hit and have a 3% chance to freeze.
A proc coefficient of 50% would mean, that your chance to stun on hit is halved
and life gained per hit is halved, too. A value of 0 means, that nothing procs on hit.This coefficient is mainly used to balance skills which can affect more than one enemy. Source
So, what's the proc rate of the Phalanx skill?
Source
So the answer is no, they will not get frozen by the bowmen.
EDIT: As of Patch 2.1, life on hit does not depend on the proc coefficient anymore. You either get the full amount on hit or you get nothing. You'll also get your life on hit only once per attack, no matter how many enemies you hit.