As Roy stated no but it may be required to be supported and secured. It is also required to be rated for sunlight resistant. For outdoor AC units the cable is permitted to be attached to the raceway feeding the unit. A few relevant NEC sections:
300.6 Protection Against Corrosion and Deterioration.
Raceways, cable trays, cablebus, auxiliary gutters, cable ar-
mor, boxes, cable sheathing, cabinets, elbows, couplings, fit-
tings, supports, and support hardware shall be of materials
suitable for the environment in which they are to be installed.
© Nonmetallic Equipment. Nonmetallic raceways, cable
trays, cablebus, auxiliary gutters, boxes, cables with a nonme-
tallic outer jacket and internal metal armor or jacket, cable, cabinets, elbows, couplings, nipples, fittings, sup-
ports, and support hardware shall be made of material ap-
proved for the condition and shall comply with ©(1) and
©(2) as applicable to the specific installation.
(1) Exposed to Sunlight. Where exposed to sunlight, the
materials shall be listed as sunlight resistant or shall be
identified as sunlight resistant.
725.143 Support of Conductors. Class 2 or Class 3 cir-
cuit conductors shall not be strapped, taped, or attached by
any means to the exterior of any conduit or other raceway
as a means of support.** These conductors shall be permitted
to be installed as permitted by 300.11(B)(2).**
310.11(B)Raceways Used as Means of Support. Raceways
shall be used only as a means of support for other race-
ways, cables, or nonelectrical equipment under any of the
(1) Where the raceway or means of support is identified as
a means of support
(2) Where the raceway contains power supply conductors
for electrically controlled equipment and is used to sup-
port Class 2 circuit conductors or cables that are solely
for the purpose of connection to the equipment control