Your dealer is right in that a power conditioner can make a system sound worse, but it's also true that a conditioner can make a dramatic improvement. Which one it is for you depends on how clean/dirty your power is, what components you use, etc. Find a way to try one or two conditioners from the better companies (i.e. Audience, Shunyata, BPC, etc.) and then you'll know. I think most (but certainly not all) people find they make improvements and have some form of condioning in their system, and then there is the added protection from spikes/surges.
I don't think someone can say difinitively whether or not to plug your amp into a conditioner. It depends on several variables, and once you have a conditioner in your system it's free to try it both ways. If plugging into the wall I'd suggest at some point having a dedicated line installed, which you should do anyway (it usually costs less than $500, which in this silly hobby is one of the cheapest upgrades you can make). And yes, a conditioner still makes a difference if you replace the stock power cords. When it comes down to it, in my experience almost everything makes a difference. Whether it's an improvement or not is another story.
I don't think someone can say difinitively whether or not to plug your amp into a conditioner. It depends on several variables, and once you have a conditioner in your system it's free to try it both ways. If plugging into the wall I'd suggest at some point having a dedicated line installed, which you should do anyway (it usually costs less than $500, which in this silly hobby is one of the cheapest upgrades you can make). And yes, a conditioner still makes a difference if you replace the stock power cords. When it comes down to it, in my experience almost everything makes a difference. Whether it's an improvement or not is another story.