No, the USPS is a Business!
the Postal Service takes on some several very non-governmental attributes via the powers granted to it under Title 39, Section 401, which include:
power to sue (and be sued) under its own name;
power to adopt, amend and repeal its own regulations;
power to "enter into and perform contracts, execute instruments, and determine the character of, and necessity for, its expenditures";
power to buy, sell and lease private property; and,
power to build, operate, lease and maintain buildings and facilities.
All of which are typical functions and powers of a private business. However, unlike other private businesses, the Postal Service is exempt from paying federal taxes. USPS can borrow money at discounted rates, and can condemn and acquire private property under governmental rights of eminent domain.
The USPS does get some taxpayer support. Around $96 million is budgeted annually by Congress for the "Postal Service Fund." These funds are used to compensate USPS for postage-free mailing for all legally blind persons and for mail-in election ballots sent from US citizens living overseas. A portion of the funds also pays USPS for providing address information to state and local child support enforcement agencies.