Canada, the US, and Mexico all have pretty nice highways. However, that isn’t the case with most Latin America countries that don’t even have paved highways. Would the supercountry use all of its resources to pave these roads, or would it just construct new ones elsewhere?
I think that many Latin American or South American countries are a lot more developed and have more paved highways than you imagine.
The Pan-American Highway1 is a network of roads stretching across the American continents and measuring about 30,000 kilometres (19,000 mi)1 in total length. Except for a rainforest break of approximately 160 km (100 mi), called the Darién Gap, the roads link almost all of the Pacific coastal countries of the Americas in a connected highway system. According to Guinness World Records, the Pan-American Highway is the world's longest "motorable road". However, because of the Darién Gap, it is not possible to cross between South America and Central America with conventional highway vehicles. Without an all-terrain vehicle, it is necessary to circumnavigate this terrestrial stretch by sea.
The Pan-American Highway passes through many diverse climates and ecological types, from dense jungles, to arid deserts, to barren tundra, some of which are passable only during the dry season, and in many regions driving is occasionally hazardous. The Pan-American Highway system is physically mostly complete and extends in de facto terms from Prudhoe Bay, Alaska, in North America to the lower reaches of South America. Several southern highway termini are claimed to exist, including the cities of Puerto Montt and Quellón in Chile and Ushuaia in Argentina. West and north of the Darién Gap, it is also known as the Inter-American Highway through Central America and Mexico where it splits into several spurs leading to the Mexico–US border.
Of course South America extends hundreds of kilometers or miles east of the Pan-American Highway in places where it is narrow, and thousands of kilometers or miles east of the Pan-American Highway in places where it is wide.
Apparently there are highways in other South American countries that are connected to the Pan-American Highway system. Thus someone should be able to drive between all the capital cities and large cities in South America.
Of course it is probable that the highway and railroad systems in many regions of South America could use a lot of improvement.
Freeways (almost) never follow the course of old highways
Very little of the old highway can be reused:
Freeways are much wider that local highways, and thus all works of art (bridges, tunnels, cuttings, fillings) need to be rebuilt;
Freeways need much stronger foundations, and thus the old highways would need to be dug up anyway;
Freeways need to be counter-inclined at curves, to allow travelling at constant high speed.
The alignment of the old highway is very often unusable:
Freeways need much larger curve radii, to accomodate higher speeds;
Freeways have lower limits with respect to slope grades;
Freeways don't go through towns and cities.
If the old highway is to be reused then a new one must be built, because freeways are long-distance interconnects and cannot substitute the local interconnects:
Freeways have minimum mandatory speeds;
Many types of vehicles are not allowed on freeways, not to mention pedestrians;
Freeways don't have exits for every little town and village.
I think what you're asking is, would the new freeways follow the course of the old freeways.
I think we can answer that "NO" - here's why...
The US went through a phase where it had "basic" roads and then indeed it upgraded to "modern freeways".
In fact, during that process, they did NOT especially follow the old roads - they improved the lines and took new lines.
So, I think that's the answer.
The US has pretty poor quality freeways currently; if for some reason they decided to spend a zillion dollars on upgrading to France- or Italy- quality freeways, I think that - just as in the historic example - they would take the opportunity to start with new lines.
Also significant: The cost of buying-out property owners would be less in South America, in your hypothetical, so there is more chance they would go to the expense of making new ways.
Are there any recent historical examples?
The building of the TGV system in France was perhaps the last time ever in the first world, that land was cheap enough for a government to scoop it up for a ways scheme?
Footnote - as others have pointed out, highways in South America are not as "bad as you seem to think". (And it's worth realizing that many/most US roads are very poor by first-world standards.)
Building a good road is more than just laying down a layer of blacktop. You need proper foundations, drainage, etc.
This all costs money so the first step would be to consider where upgrading the roads is the most important.
Then how the upgrade should happen. Is there a strip of land that the new road can be built on? Can part of the road be closed while the foundation works are happening? How to handle the congestion during construction? The answers to those questions all depend on the road being upgraded.
This all assumes that the umbrella government actually gives the Latin American side the money needed to upgrade the road infrastructure on that scale. It is possible that the merger doesn't include road infrastructure support and that they have to get the funds for each upgrade on their own.