Must A Copyright Holder Attach The Deposit Copy To Its Complaint?

No.  Rule 8 (i.e. notice pleading) is alive and well in the copyright context.

PK Studios, Inc. provided architectural drawings for homes to Stock Development, LLC in connection with development in two communities.  PK provided a release to Stock allowing it to use the architectural drawings for the two communities and for any other projects developed solely by Stock.

Ten years later (in 2014), PK discovered another community being developed by other parties which PK claims are "exact duplicates" of the drawings it had provided to Stock a decade earlier.  PK notified the developers of this new community, who responded that they received a license from Stock.  But PK states that Stock was not authorized to provide such a license.  So PK sued all sets of developers.

The developers of the new community sought dismissal on the pleadings, arguing that PK did not sufficiently identify the work because it did not attach the copy of the drawings it had submitted to the Copyright Office.  According to the defendants, this did not provide sufficient notice to them in order to frame a response.  The Court did not agree:

While the Court agrees with Defendants that PK Studios cannot ultimately prevail on this count without providing the specific materials alleged to have been copied so that they can be compared to the Eagles Landing designs, PK Studios was under no obligation to do so at the pleading stage, In re Southeast Banking Corp., 69 F.3d 1539, 1551 (11th Cir.1995) (Rule 8 does not “impose upon plaintiffs the burden to plead with the greatest specificity they can”), and Defendants will be able to obtain this information during discovery

Motion to dismiss (or for a more definite statement), denied.

PK Studios, Inc. v. R.L.R. Investments, LLC, Case No. 2:15-cv-389 (M.D. Fla. Jan. 4, 2016) (J. Steele)