Will a "commercial use" of the invention be considered "public use" under 35 U.S.C. 102(a)?

Yes, a commercial use of the invention by the applicant before the critical date, even if such use does not make the invention itself a matter of public knowledge, is considered sufficient to invoke the statutory bar. See Special Devices, Inc. v. OEA, Inc., 270 F.3d 1353, 1357 (Fed. Cir. 2001).  Suppose, for example, that the applicant invented a more efficient method of manufacturing copper wire. If the finished product resembled any other copper wire, no one outside of the factory might know anything of the improved process. Nevertheless, if the applicant used that process, and profited from it, prior to the critical date of the patent application, the Federal Circuit has held that such use forfeits the right to obtain a patent.  D.L. Auld Co. v. Chroma Graphics Corp., 714 F.2d 1144, 1147-48 (Fed. Cir. 1983).