I think so, yes, by my definition of spirituality as how one feels and/or relates to something or indeed 'everything.' (Everything as in the universe, the essence of life, or the totality of being etc.)

One can have a spiritual connection with a work of art, in the sense that a feeling is engendered by the use of colour, line etc (beyond the immediately apparent.) A feeling of wonder, or awe, sometimes beyond explanation in purely logical terms. If I look at a Jackson Pollock or Mark Rothko painting I can see or feel it as metaphoric in some sense to any number of concepts, purely as metaphor. This doesn't contravene logic because I'm not claiming it (or understanding it) to be anything more than metaphoric or analogous. If however I say that 'that's actually an exact likeness of The Eiffel Tower, or Dwight D. Eisenhower' then that would contravene the principles of logic because a quick perusal of photographic evidence of the originals and comparison to the artwork would falsify my claim.

Neuroscience is making progress all the time in respect to neurotransmitters and how what we know as 'feelings' can be explained in pure logic and biochemistry. We might one day find that it's just a bunch of peptides or just neurons passing information, but I venture that we'll still 'feel' a certain spirituality in some sense. Even if it's just within the everyday; love, compassion etc.

People can and do relate spiritually to any number of things. In a free world, they must be allowed to. I'd posit that the boundary where spirituality causes a fault in logic is only reached when that spirituality is taken not as a relationship but as a stone cold fact in the objective, without evidence; either through empirical science or logical reasoning.