First of all it should be noted that an ayllu is technically one community in the Andes, set up in one region/climate zone. Ayllus did get together in daisy-chains of communal marriage and trade across climate zones (east-west), allowing for broad trade of good from the Amazon's fringes (and perhaps deeper) all the way to the Pacific coastline. Adding ayllus to cooperate within this "vertical archipelago" could get high Andean potatoes, mid-elevation coca and corn, fish and salt from the coast, tropical fruit and exotic fauna from the forest...a quite diverse range. So in that sense of your question, yes, the ayllus traded thoroughly.

While ayllu chains certainly worked quite strongly along their cross-climactic, generally east-west lines, the spine of the Andes is north-south (more or less). While the treacherous rivers (especially the Apurímac) inhibited travel along their courses in places, moving over high puna plateaus and in the less steep valleys was quite possible. The Qhapaq Ñan, a series of over 20,000km of roadway maintained by the Inca by mita labor tax, built many of these by expanding and following already-existing roads from prior cultures - especially the Wari and Tiwanaku, who had some serious montane expansions of their own some seven or eight hundred years before.

Now, there is a question of how long the ayllu system is. In the past the ayllu has been hailed as "Andean socialism" and an enduring tradition that can help explain interactions in the Andes through millennia. However there has been some recent pushback on this notion - it's quite direct-historical (assuming socioeconomic structures came from somewhere and can be a model for interactions that preceded these socioeconomic structures' earliest documentation). It's been proposed alternatively that the ayllu system was put in place by the Inca, in cooperation with local communities; at the very least the ayllu network was at its strongest during Inca times. So if we let go of the idea as ayllu explaining everything we need to know about trade and community building in the Andes across all its vast space and time of occupation...we can think a little more about where else Andean communities and cultures wanted to trade, where they moved. Looking at the Qhapaq Ñan once again, the stoutest roads most maintained by the Inca (for military, yes, but also economic purposes) move north-south; this benefitted the Inca, to be sure:

A slice of food was being lifted to [Atahualpa's] mouth when a drop fell on the clothing that he was wearing. Giving his hand to the Indian lady, he rose and went into his chamber to change his dress and returned wearing a dark brown tunic and cloak. I approached him and felt the cloak, which was softer than silk ... He explained that it was made from the skins of bats that fly by night in Puerto Viejo and Tumbes and that bite the natives. [Pedro Pizarro 1986, translated by Hemming 1970]

To be clear, Tumbes is a small coastal region that straddles the modern border of Peru and Ecuador. In this case and in others, goods of any one community could have been traded north-south, even great distances - but at the behest and within the priorities of the Inca nobility. Thus while Tawantinsuyu flourished in its production east-west (along with all the trade and kinship that went to strengthening any one daisy-chain), the really incredible trade power flowed north-south.

As a final neat little point for your consideration, let's consider some non-material rationales for moving north-south in the Andes. Mountains in the Andes have been considered apu, the great ancestors of all people born there, for many centuries as well. Sent out from their caves from the central navel at Lake Titicaca by the Creator Wiraqocha, apu birthed, sustained, and sheltered all of their communities, and were highly revered for it. Patrick Ryan Williams wrote an intriguing article ("Sighting the Apu", 2006) regarding the selection of Wari sites in relation to the landscape. These mountaintop fortresses throughout their area of control all had serious site alignments to visible apu on the horizon.

Modern ethnographies have determined that while many mountains are apu, some (the tallest, stoutest peaks of the two cordilleras) are considered some of the strongest, oldest deities. Williams proposes that by aligning themselves to nearby and distant apu, they keyed themselves in somewhat coercively to the veneration and connection of both local and regional communities. Keeping several of these large apu in sight by multiple Wari centers (or at least one) would have been a profound statement to any clients - "we are in control of your ancestors, and we venerate them." Such methods of political authority generated by co-opting local deities and pantheons allowed the Wari to spread across much of the central Andes. With all this in mind, while the east-west "vertical archipelagos" of ayllus are interesting - and fruitful - economic and political endeavors, many of the truly remarkable and enduring cultures of the Andes have been those that could curry these relationships and motivate them across the great north-south avenues, as these carried extra weight ideologically and cosmologically.