‘Annan Sahadi’ in receiving a commandment

There is no reason not to. An Sahadi replaces a requirement for testimony so he can replace a requirement for speech, as long as speech is only required to convey the information. If the requirement is formal that one must speak, then thought may not be sufficient. For example, in the case of conditions, things that are in the heart and in the heart of every person do not need to be spoken (see Tos Kiddushin 7 and many more).
Although the situation regarding conversion has changed in recent generations. In the past, there was a presumption (Anne Sahadi) that someone who came to convert probably truly believed and wanted to join us for proper reasons (and even if he did so because he wanted to marry someone, it used to be clear that he would have to join the group of observant Jews. All Jews used to be like that). Today, people have an interest in joining (for example, to receive immigrant rights and the Law of Return). Therefore, it is clear that today there is no such presumption. This does not mean that everyone comes for improper motives, but there is no longer a presumption that their motives are kosher.
You can search for the articles “The Gates of Conversion – Violence and Good Intentions” here on the site.