This is a common question which has two answers. First I will address the legal answer.
The NFA restricts transfers of weapons. Normally we would not think of loaning a firearms or placing it in the hands of another person as a transfer, but under a more complete analysis, letting someone else use your silencer or other NFA firearm, is in fact a transfer and a violation of the National Firearms Act.
The NFA defines a transfer and the various derivatives of such word, to include selling, assigning, pledging, leasing, loaning, giving away, or otherwise disposing of.
Many individuals incorrectly read the definition to state that loaning is only when otherwise disposing of, but otherwise disposing of is just another action that creates a transfer and is not a requirement of the previous terms or actions that are included in the definition of a transfer.
Prior to a transfer, the owner, trust, corporation, or individual who has the legal title to the NFA firearm, but pay a tax and receive permission to transfer the firearm.
In addition the NFA states that it is illegal to receive or posses a firearm which is not registered to him in the National Firearms Registration and Transfer record, to transfer a firearms in violation of the law, or to receive or posses a firearm transferred (including loaned per the definition of transfer) to him in violation of the NFA.
The NFA requires no intent to violate the law to create a violation.
So perhaps the better question is Should I let someone else use my silencer? I think the clear answer to this is no, unless it is done in a way that does not create a transfer or a violation of the NFA.
Do people let others use silencers? Yes it is common and probably will not result in a penalty, but unlike speeding, which is done regularly, the fines and potential penalties for transferring a firearm restricted by the NFA is very substantial. The instructions provided with our Gun Trust explain these and other related issues involving inadvertent transfers of NFA Firearms.