Cyclists DO produce emissions. In some cases rather more than one might think!
Consider A NSL SC road with traffic traveling in both directions.
Consider an HGV traveling at 40 coming up behind a cyclist.
The HGV will require a gap in the oncoming traffic in order to pass the cyclist. Sometimes there is one, sometimes one can plan for one, but if the road is busy more often than not one will not be available when it is needed so the truck will have to slow down and wait for one,
Slowing from 40 to (say) 12 and then accelerating back up to speed will consume around half a litre of fuel that would not otherwise have been consumed!
If in the course of (say) a 7 mile cycle ride this scenario is repeated more than a couple of times our cyclist would have produced less "Emissions" by leaving his bike at home and driving a Range Rover Sport instead!
The same scenario also applies to cars. though the overall effect on lighter vehicles is less dramatic individually. overall the effect is quite large owing to the large numbers of such vehicles. Though it would be difficult to quantify I suspect that only a small increase in the use of cycles on extra urban highways, unless proper segregated cycle lanes are provided, will actually significantly increase national emissions and fuel consumption.