No, it won't work. The 99 model never came with Bose - the premium system in 99 was the Monsoon. Bose systems use special head units with pre-amp level output but Monsoon systems use ordinary Delco HUs with speaker level output.
Third generation Bose systems were more like the Monsoon - an ordinary head unit with an external amp and different speakers. Fourth generation Bose (93-96) used special head units with low-level, high-impedance output that are not plug-and-play interchangeable. There are adapters that will allow replacement of the special bose HUs with a standard one.
Third generation Bose systems were quite a bit different from the early fourth generation Bose. 93-96 Camaro Bose systems had either three or five speakers (depending on option code) with individual amps attached to them. The head unit output low-level, high-impedance (something like 18-ohm) signal to the individual amps which were attached to very low-impedance speakers.