Yes. Attachment to objects can be a general (a particular item but all examples of that item) or very specific (one specific item and no others will do, regardless of how similar they are).
Here are a couple of previous asks we’ve had about this topic:
http://askanautistic.co.uk/post/125856202174/is-getting-emotionally-attached-to-objects-and
http://askanautistic.co.uk/post/125161654294/why-are-autistic-persons-so-attracted-to-their
I think their are stereotypical objects autistic people tend to general gravitate too like rubix cubes and such, I personally as an autistic person got attached to the conman house-hold slinky, even to this day as 23-year old I still play with it on a daily basis :L so the object itself will definitely vary but I think every autistic person has the ‘one object’ they’re fond of