You might want to refer to 6.2.3.2. for acceptable materials in air duct systems:
https://www.ontario.ca/laws/regulation/120332
They typically have to be constructed from metal materials, but can be constructed from combustible materials provided they meet the following requirements:
(2) Ducts, associated fittings and plenums are permitted to contain combustible material provided they,
(a) conform to the appropriate requirements for Class 1 duct materials in CAN/ULC-S110, “Test for Air Ducts”,
(b) conform to Article 3.1.5.15. in a building required to be of noncombustible construction,
(c) conform to Subsection 3.1.9.,
(d) are used only in horizontal runs in a building required to be of noncombustible construction,
(e) are not used in vertical runs serving more than 2 storeys in a building required to be of noncombustible construction, and
(f) are not used in air duct systems in which the air temperature may exceed 120°C.
The major challenge they are likely to face is (a). Chances are the underside of your cabinet has not been tested to that standard.
Similar language in NBC Part 9.
9.33.6.2. Materials in Air Duct Systems
1) Except as provided in Sentences (2) to (6) and in Article 3.6.4.3., all ducts,
duct connectors, associated fittings and plenums used in air duct systems shall be
constructed of steel, aluminum alloy, copper, clay or similar noncombustible material.
2) Ducts, associated fittings and plenums are permitted to contain combustible material provided they
a) conform to the appropriate requirements for Class 1 duct materials in CAN/ULC-S110, “Test for Air Ducts,”
b) conform to Article 3.1.5.18. and Subsection 3.1.9.,
c) are not used in vertical runs serving more than 2 storeys, and
d) are not used in air duct systems in which the air temperature may exceed 120°C.
The only "get out of jail free" condition is (6)
6) Except as provided in Sentences 9.33.6.13.(2) and (3), ducts that are part of a
return-air duct system and that are contained entirely within a dwelling unit need not
comply with the requirements of Sentences (1) to (4).