Q: Does iTunes have record of a serial number on a missing itouch?

You can find the SN here:

iPod: How to find the serial number

You can also go to iTunes>Preferences>Devices and hover the mose pointer over the iPod backup and the SN will come up

Apple will not help track, block or do anything for a lost/stolen iPod. See:

Reporting a lost or stolen Apple product

No the serial no is not on itunes

but what u can do is call apple and they will lookup the info using name and info etc