Does building of military roads go faster with larger legions?

You need at least 5 cohorts to build a road.

Roads are buildings visible on the map that increase army movement speed by 50%. ... An army with the tradition and at least 5 cohorts will be able to begin building a road toward another city. While building the road, the army movement speed will decrease to 20% and morale will be lowered too.

So the road is built depending on how long it takes the army to arrive as its destination.

It might be the case that some units or techs mean armies move faster (on the campaign map) meaning roads are built quicker.

An easy way to increase road building speed (if you need to build lots of roads), is to break down larger armies into multiple smaller armies. This allows you to build many roads simultaneously.