I have been trying to write music that does not resolve to a tonic. Would this be non-functional harmony?
CMaj7 / Dbdim7 / BMaj7 / Eb7b5
Your terminology is incorrect. Normally we speak of a chord resolving: not a series of chords. Though it is true that your chords have not (yet) given any indication of a tonic.
None of your chords - Maj7, dim7 and 7flat5 - have 'functions', but it is not an example of 'non-functional harmony'.
The term 'non-functional harmony' comes from classical music, and applying it to other types of music is risky. According to the rules of harmony a dominant seventh had to be immediately resolved. G7 had to lead straight to C (or Cm), for example. After Bach's time all the rules were gradually eroded. Dominant sevenths didn't always resolve 'correctly'.
In Debussy's La cathédrale engloutie, at 4'50", (at the word 'molto' of 'molto dim') there begins a series of ten dominant seventh chords, none of which resolve. These chords aren't there to perform their traditional function. They are non-functional. It was their colour, their weight and their texture that Debussy wanted. It's very like a C20th artist painting for the sheer love of colour rather than to represent something.
We are used to such music now, but in 1910 it was unusual. There had been many earlier examples of dominant sevenths not resolving, in Mahler for example, or in Liszt's more experimental piano music; just as in painting there had been Turner, the Impressionists and others. But Debussy's writing a whole string of them was unusual. His prelude is tonal - it's clearly in the key of C - yet here in the middle of a piece, beginning with that chord of D#7, we are a long way from home. In fact the music seems to have lost its way home. Worse - it doesn't even seem to be interested in going home. Early audiences would have found that disconcerting.
In blues/jazz/rock music the term 'non-functional harmony' is as meaningless as it has been in the context of 'classical' music since Schoenberg.