It does seem implausible doesn't it and better access to the airport is not the primary reason in the mind of the Lib Dem led Bristol City Council that formally objected to the airport's expansion planning application last year: fortunately for the airport it's situated in the area of the North Somerset unitary authority who disagreed.
The South Bristol Link Road will be for general traffic though not a dual carriageway. Already the environmentalists are up in arms about the green land it will be built over.
The grandiosely named Bristol Rapid Transport system that will feed into the link road from the main central railway station is intended solely for buses on a guided busway and may feature the Airport Flyer. The city really wanted a tram system but lost that chance years ago when the local authorities that make up the conurbation failed to agree on routes so the promised central funding for that was withdrawn.