The short answer is yes, peasants made up the majority of the USSR's population in the late 1920s. The slightly longer answer is still yes but with the caveat that the 1920s was a period of great social movements and demographic flux.

The 1920s began with the demographic crises of the Revolution and Civil War. The, admittedly war-inflated, urban population plummeted as hunger, shortages and mass unemployment bit deep. By 1921 the populations of major cities, ie Petrograd and Moscow, had fallen by approximately 50% from their 1917 peak; lesser cities suffered similar, if not as severe, falls. In the face of extreme hardship millions of Russian urbanites simply fled to cities for the perceived security of the countryside. The relative youth of the Russian working class, while easy to overstate, facilitated this – many workers had recent roots, and often land, in their villages of origin.

An end to the Civil War and the progress of the NEP in the early 1920s allowed some recovery from this disaster. However according to the 1926 census some 82% of the Soviet population lived outside towns and cities – almost the same percentage as in 1897. For all the growth of the pre-war years and the NEP, Russia was still an overwhelmingly rural country. In many ways the Revolution had, by removing the noble estates, actually strengthened the traditional landowning patterns and ways of life.

But we can't stop at 1926: the Soviet Union was about to plunge headfirst into another disorientating and wrenching change, this one inflicted from above. The advent of Stalinist industrialisation saw mass migration into the cities on an unprecedented scale. Between 1926 and 1939 the urban population more than doubled as peasants flocked to the cities for work. In this they both encountered dire conditions – investment in living conditions never being a priority for the Stalinist state – and themselves transformed the cities they arrived in: a creeping 'peasantisation' of Soviet life, to borrow Lewin's phrase. Yet such was the previous imbalance in the economy that by 1939 some 77% of the Soviet population still lived in rural settlements.

So, yes, the considerable majority of the Soviet population in the 1920s and 1930s consisted of rural peasants. This was quickly changing but would take another few decades for it to become a predominately urban society.

As a note, I've tended to talk about the rural/urban split above because it avoids the thorny question of that constitutes a peasant. For example, the peasantry was a formal estate under Tsarist law but this included urban workers and professional soldiers, while excluding some of those engaged in small agriculture, eg Cossacks. This is not very helpful. Easier to accept instead that the vast majority of the rural world would have been occupied with agricultural production or otherwise closely linked to this peasant milieu.

Sources:

• Davies et al, The Economic Transformation of the Soviet Union for the numbers

• Moon, The Russian Peasantry 1600-1930. This has a pretty good discussion on the definition/categorisation of the peasantry.