Is it possible (for me) to channel someone’s conscious mind and, if so, what would happen in terms of their awareness?

This again is a clever and quite creative insight. The answer is yes, it is possible, and as you predict they would be aware of you within their mind seeking access and wanting to speak with them. They might interpret this as a break with reality, so we do not recommend you do this on the unsuspecting as it could be quite disturbing, but as a parlor trick you can try this for yourself and explore the possibilities and will learn from this, accordingly. The utility is quite limited other than for communication at a distance, but there may be a time and place for this in certain circumstances, as well. There are individuals who are in desperate straits who are lost and who are being held against their will, and so forth. To be able to connect with them and perhaps learn important clues about their circumstances and help to give them reassurance would, to be sure, be a blessing and would represent fine work indeed.