Yes, a person owning adjacent parcels of real estate can establish a party wall agreement between them, although in my experience, when an agreement of that type is established by a common owner, rather than different owners, it is usually titled a "Declaration" rather than a "Party Wall Agreement" (for obvious reasons). This is basically a maximally simplified version of how condominiums and "planned communities" in large subdivisions are typically established.
It would generally be best to give notice to yourself, even though it seems silly, because it allows you to show compliance with a statutory check box for compliance with the law. It also wouldn't be uncommon (and indeed would be prudent) to establish a separate holding company to own each of the adjacent parcels (both for liability protection reasons and so that there would, superficially and formally at least, be two separate owners of the adjacent parcels).
I have a case pending right now in the Colorado Supreme Court on a similar issue where property was subdivided into separate parcels by a common owner and one of the issues is whether the common owner complied with a statutory requirement to give notice to himself in the manner required by law. I suspect that my client will win on that issue, but if his predecessor in title had simply given notice to himself as required by statute and kept proof of doing so, this case might never have gone to court, instead of having to be litigated to the second highest possible appellate court in the land, saving huge amounts of money and time and aggravation and this would have made his successor's title more secure.
Usually, this is done in anticipation of the future sale of one of the parcels. Sometimes this is done in anticipation of one or more of the units being leased with ownership-like responsibilities falling upon the tenants (e.g. in the case of a typical triple net lease where almost all ownership costs are the responsibility of the tenant). It could also be relevant to the property insurance underwriting of the parcels and to how insurance companies allocate responsibility if separate policies of insurance by separate insurance companies are issued for each parcel.