Does TitleLeaf store a publication date?

No, TitleLeaf doesn’t have a publication date field in its database. As an opinionated implementation of ONIX, TitleLeaf derives a publication date from the status and the release date of a given product format:

If the status is “PC” or “PP”, then the publication date is blank
If the status is not “PC” or “PP”, then the publication date is defined as the release date

See ONIX List 163: Publishing date role, value 01:

Publication date: Nominal date of publication. This date is primarily used for planning, promotion and other business process purposes, and is not necessarily the first date for retail sales or fulfillment of pre-orders. In the absence of a sales embargo date, retail sales and pre-order fulfillment may begin as soon as stock is available to the retailer