It is not the usual style, because most converts are simply acting for religious motives, and openly live their faith. However, the Islamic religion specifically allows for a strategy of hiding ones beliefs, if necessary. This is "taqiyya" (dissimulation). As they say: "It is permissible to speak words of unbelief when al-Taqiyya is mandatory." Taqiyya is especially assciated with the Shia, and they get criticised by the Sunnis for it (it is like the Catholic/Protestant thing "you can't believe what a Shia tells you! They practice taqiyya!) In fact, this custom is found in many Islamic sources, the Shia were more into it because they were a minority and often persecuted. As a stragegy, taqiyya is simply part of the accomodating nature of many Islamic beliefs - it is meant to be an easy religion - and does ask people to stick their neck out un-necessarily.
But you can see how the taqiyya rule could be changed into the means of preserving some cultish, secretive, Islamic organisation which might recruit a man like McVeigh. If he converted, he did not join the line up in an ordinary mosque.