in your experience of Islam, have you found that such a claim is warranted?
No, the claim is not warranted.
Muslims can't have it both ways:
They can't both be the fastest growing religion in the world and have a book that obligates them to have an in-depth understanding of an Ancient Dialect of Arabic, which very few people have. (this is,after all, the foundational argument made by them when you criticize it, so by default HAS to be the foundation of accepting it.)
They can't both be the fastest growing religion in the world and then say 'they are not muslims' whenever a muslim does something bad.
They can't both be the fastest growing religion and have over 300,000,000 illiterates who 'know the quran is perfect and true'.
(a contradiction)
Almost all of the increase in population is down to birth-rates, where children are indoctrinated by over-zealous parents into the Islamic faith; there are very few permanent exceptions.
The general rule in regards to Islam (infact any religion) is that all it takes to be a part of it, is to call yourself one;
There seems to be absolutely no requirement in understanding the religion or following it to any extent from that point on.
For example: Only 1/10 Christians have ever even read the Bible (to absolutely ANY extent,I assume) yet still consider themselves Christians.
When you apply even the most BASIC necessities on a belief system (such as being able to read, being at an age to understand it, following the most basic of rules etc etc), the final population is reduced by upto 1/3 each time.