Do the mechanicum mistake AI for machine spirits?
No i don't think so. Rather i would argue that there are real machine spirits because of the way the 40k universe works. The power of belief is a real thing in 40k and machines have a real 'spirit' because everyone believes they have a spirit and thus it becomes true. there has been a Horus Heresy book that features real AI and that displayed to be vastly different from all the other machines.
Furthermore one of the reasons it not real AI is because of the effects a machine spirit can have on a human interfacing with it. In a Titan it can be that the spirit literally influences the operators emotions and behavior, this is most common with Titans and Knights. It seems that the bigger the machine the more powerful the spirit.
There are examples of lesser machine spirits which make a weapon malfunction more/less which happens more often with tanks or larger weaponry.
edit: there is a example of a low level AI along with a machine spirit in the imperial military, the space marine land raider is capable of driving and firing on its own, albeit to a lesser degree than when manned.
source:
Warhammer 40,000: Rulebook (4th Edition), pg. 25
Warhammer 40,000: Rulebook (5th Edition), pg. 81