Auxiliary constructed languages are meant to be learnt faster than natural languages.
Are there convincing examples that auxiliary constructed languages are in fact easier to learn than natural languages?
Some auxiliary languages are easier to learn than natural languages. There have been many experiments that show that Esperanto is both easier to learn than other languages, and also makes learning future languages easier.
Two quotes from some of the experiments on Esperanto:
"It is possible for the average student to understand written and spoken Esperanto in 20 hours better than he can understand French, German, Italian, or Spanish after 100 hours."
"A child can learn as much Esperanto in about 6 months as he would French in 3–4 years... if all children studied Esperanto during the first 6–12 months of a 4–5 year French course, they would gain much and lose nothing."
However, it's not necessarily true that auxiliary languages are meant to be learnt faster than natural languages. Esperanto is a very regular language, and that makes it easy to learn. Other languages, such as Interlingua, are not as easy to learn, but are meant to be more recognizable to someone already familiar with the vocabulary of Romance languages. It is still more regular than the natural languages it's based on, so it likely is easier to learn, but it sacrifices some regularity in order to have a more familiar vocabulary.