Yes, it is possible that the statement could be thrown out--and if it was the only evidence for the charge, the charge itself dismissed--IF the person can be shown to have been so intoxicated as to not be mentally competent at the time. Merely having taken a mind-altering substance does not automatically invalidate the statement; there must be evidence (e.g. an expert opinion by some relevant medical expert or practioner, who examined the person at the time or reviewed blood, etc. tests taken then) to show that the person was not legally competent at that moment.