Not really so much as Catholics would like to put forth. They were more often autonomous assemblies (ekklésia) which really has no relationship to what is understood as "church" today.
>>"Kataholos" of course translates into ... you know...<<
Um,,,,,actually no. The Greek word for Catholic is katholikos not Kataholos.
The words kata and holes are two different words. Kata meaning "throughout" and holes meaning all or the whole. When they are used regarding the assemblies they are referring to multiple assemblies not just one organization as in Acts 9.
Acts 9:31 Then had the churches (ekklésia) rest throughout (kata) all (holos) Judaea and Galilee and Samaria, and were edified; and walking in the fear of the Lord, and in the comfort of the Holy Ghost, were multiplied.
The Greek word katholikos is not found in scripture. The first time that word is used regarding the believers is years after the death of John and only refers to the universality of like beliefs.
Any attempt to inject the word "catholic" into any references in scripture is a tortured twisting of the words.
"Katholikos" is an adjectival form of the same term.
They were simply descriptive of the church, before they were conceived of as a denominational term.