First off the census is used for determining how many seats are used for congressional apportionment and allocating federal funds.

So unless you're willing to also say that counted illegals cannot used for either of those, then you're just being obtuse.

But if we can agree that they cannot be used for that then sure, lets identify and count them. If we can't identify (make non-private) and count them then why should we trust that those counts are accurate?