Rich, I think you hit the nail right on the head when you said "...is it really possible to remove these ticks and pops, or at least the ones caused by contamination..." There are two sources of clicks and pops on a record those caused by a foreign body sitting on top of the grooves and those cause by an imperfection in the grooves themselves (such as a scratch). Certainly if the pop is caused by something sitting on top of the record, cleaning the debris off will get rid of the noise. However; if the noise is being cause by any kind of surface defect, whether caused by the pressing process or some other external force, no amount of cleaning is going to get rid of that click.
That said I have to agree with Bob, there is really nothing like a clean record. While it may not get rid of all the clicks and pops, a good cleaning will lower the overall noise floor and give you a blacker background. I really don't know sonically what the difference between a vacuum based cleaner and one of the newer hand type cleaners. I heard what the VPI cleaners could do 20 years and was sold on the spot. I have been using it ever since and swear by the results. Some of the newer hand systems may come closer than the ones that were around 20 years ago, but I have never really tried them because, well, I already have the 16.5.
On a theoretical basis a vacuum system will work better for two reasons. First it will allow you to use cleaner formulas that may do a better job cleaning but would damage the record if left on for an extended period of time (the vacuum will do a better job of removing all residue of the cleaner as compared to soaking it up with some kine of rag or pad.) and secondly the vacuum will life any dirt out of the grooves instead of pushing it back down like a pad might do when it is drying a record. While all of this sounds good on paper I can't say that I have ever done any first hand A/B testing between the 16.5 and any of the currently available hand cleaning systems.
The 16.5 is bulky, noisy and not cheap, but it does a great job and if you want mine you are going to have to pry it from my cold, dead hands.