Please join me as we take a trip deep into the weeds.
Fact - the People are required to serve a 710.30 notice when they intend to use statements of the defendant, which meet other criteria which will not be enumerated here.
Fact - Sometimes the People do not serve a 710.30 notice as to some or all statements meeting those criteria.
Fact - The Appellate Division, Fourth Department, has ruled that using such statements for the purpose of impeachment is perfectly okay even so (People v Pruitt, 6 AD3d 1233 [4th Dept, 2004] ["Contrary to defendant's further contention, a CPL 710.30 notice was not required because the challenged statement was elicited during rebuttal and was 'offered solely for the purpose of impeachment' (People v Hill, 281 AD2d 917...)"]). Note that this wasn't simply impeachment of a defendant during his testimony, but elicited during rebuttal, conceivably to impeach someone other than the defendant, though probably to impeach the defendant. A fortiori, if there is an un-noticed statement it can be used in direct impeachment of the defendant who testifies on his own behalf.
Where the People serve no 710.30 notice, the defendant cannot move to suppress, or else he forfeits his right to preclusion under 710.30. Therefore, if the only issue were notice, every un-noticed statement would be uniformly admissible regardless of the circumstances under which it was obtained. Police could literally beat a statement out of the defendant and, on this analysis, use it to impeach. This can't be the law.
What the prosecution would no doubt like is this: where there are issues of true voluntariness, such that a statement would not be usable even to impeach, the defendant must allege such when the statements are offered. This, however, represents a motion to suppress, which immediately forfeits the defendant's right to preclusion. Therefore, in my view, this would unduly burden the defendant's federal and state constitutional rights, which prohibit the use of truly involuntarily obtained statements, by requiring the defendant to forfeit state in order to protect constitutional ones.
In my opinion, and here's the shiny object in the weeds that I wanted to get to, the People have a burden under People v Huntley (15 NY2d 72 ) to establish that the statement is voluntary before it can be admitted:"the jury passes on voluntariness only after the judge has fully and independently resolved the issue against the accused’ and has made express findings upon the disputed fact question of voluntariness." 710.30 doesn't reduce the People's burden on voluntariness from beyond a reasonable doubt to nothing whatever. The defendant should not be deprived of this constitutional right by requiring him to forfeit his state statutory right in order to exercise his federal right. Using an un-noticed statement, it seems to me, represents a due process violation not because the statement should be suppressed, but because it should not be admitted without proof that it was not involuntarily obtained, which the defendant need not even allege because to do so would improperly require him to forfeit other rights.
It might still be worth making a suppression motion mid-trial, certainly if there is potential proof on your side that the statement was truly involuntarily made, and potentially if the normal Huntley motion can be made (I am somewhat uncertain about this - it's a esoteric part of an obscure topic), i.e. move to suppress without specificity. The People's inconvenience at this point is due to their failure to serve notice.