Do you know of anybody who has converted to Islam but kept the conversion secret? That doesn't seem to be the style.
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.