Meaning of "if not" in a sentence

This turned out to be a bit more complicated to explain than I had anticipated, so I can understand the reason to post your question on ELU! The combination of "if not", "invoking" (which lends a sense of something not present) and "presenting" (i.e. being present) takes some unravelling…

if not - ODO:

Perhaps even (used to introduce a more extreme term than one first mentioned):
'hundreds if not thousands of germs'

invoke - ODO:

2.2 Give rise to; evoke:
'how could she explain how the accident happened without invoking his wrath?'

So, your bolded portion could be reworded as:

organ versets replaced the chants, but as they were based on the words of the chants, the versets evoked [gave a sense of] the words without actually presenting them.

If not, in gerneral terms represents a more extreme term than the former (in this case 'invoking'). Organ chants were based on the chants they replaced, thus invoking perhaps even presenting the appropriate words.

In this case, 'presenting' is more extreme than 'invoking' the appropriate words.

For example: Let's meet up tonight if not sooner (link).