If the unit is undersized by a large percentage, of course cooling effect will diminish.
But stating that NO COOLING will result is completely false.
When relative to the same camper with no cooling at all, the one with the AC unit, even severely undersized, will always be cooler.
By how much is your only variable.
The simple fact is that the vast majority of folks that are interested in AC units (many who start and respond to these types of threads) are in the small to medium size camper range.
That range puts the ideal BTU output for an AC below 5k BTU. This is what the industry is lacking right now.
2-3k BTU units would be ideal for this crowd, and would satisfy the needs of 90+% of the typical truck campers and small tow trailers.
Dropping to that ideal BTU rating creates two things.... a MUCH more efficient camper that is considerably easier to manage and maintain temps and humidity levels,
and a cooling system that most would be considerably easier and realistic to run using solar and a decent battery bank.
A simple calculator that can be used to show just how many BTU you need for your specific space can be found here:
http://www.calculator.net/btu-calculator.html