Something to keep in mind - the AdMech believes in the notion. The entire AdMech, galaxy wide, with most in the Imperium also buying into the concept. For over ten thousand years.
Given how the Warp works, the collective belief in the concept for so long makes me reluctant to discount the concept. Likely machine spirits do exist as a thing in the Warp, though they're rather variable. Things like age, complexity, frequency and importance of use, and level of veneration all likely affect the power and complexity of the machiy spirit. Most are likely equivalent to dumb animals, but something like a really old Titan may well have a strong soul and awareness as a result.
The funniest thing is that this belief is largely a human only one, and that it's specifically aimed at human made tech. It may well be the case that only human made tech has machine spirits, and pure xenotech doesn't.